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94-443: Greek astronomers used the dioptra to measure the positions of stars ; both Euclid and Geminus refer to the dioptra in their astronomical works. It continued in use as an effective surveying tool. Adapted to surveying, the dioptra is similar to the theodolite , or surveyor's transit, which dates to the sixteenth century. It is a more accurate version of the groma . There is some speculation that it may have been used to build

188-586: A praefect architectus armamentarius of the apparitor status group (a branch of the Roman civil service). He is mentioned in Pliny the Elder 's table of contents for Naturalis Historia (Natural History), in the heading for mosaic techniques. Frontinus refers to "Vitruvius the architect" in his late 1st-century work De aquaeductu . Likely born a free Roman citizen, by his own account Vitruvius served in

282-432: A Marcus Vitruvius Mamurra have been suggested as evidence that Vitruvius and Mamurra (who was a military praefectus fabrum under Julius Caesar ) were from the same family; or were even the same individual. Neither association, however, is borne out by De Architectura (which Vitruvius dedicated to Augustus ), nor by the little that is known of Mamurra. Vitruvius was a military engineer ( praefectus fabrum ), or

376-615: A book On the Sizes and Distances of the Sun and Moon , which is his only work to have survived. In this work, he calculated the sizes of the Sun and Moon, as well as their distances from the Earth in Earth radii . Shortly afterwards, Eratosthenes calculated the size of the Earth, providing a value for the Earth radii which 252,000 stades , which may be equivalent to 39,690 kilometers, rather close to

470-411: A circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square. It

564-458: A description or quotations. Some elementary works have survived because they were largely non-mathematical and suitable for use in schools. Books in this class include the Phaenomena of Euclid and two works by Autolycus of Pitane . Three important textbooks, written shortly before Ptolemy's time, were written by Cleomedes , Geminus , and Theon of Smyrna . Books by Roman authors like Pliny

658-520: A geo-heliocentric system, where the sun rotated around the earth, but all other bodies rotated around the sun. Finally, in the 3rd century BCE, Aristarchus of Samos (sometimes called the "Ancient Copernicus " ) was the first and only premodern figure to propose a truly heliocentric model of the Solar System , placing the sun, not the earth, at the center of the universe. Plato and Eudoxus of Cnidus were both active in astronomical thought in

752-430: A pair of concentric spheres. That is to say, that both heaven and earth are conceived of as a sphere which have the same center. In this way, they resemble the structure of an (conceptually spherical) egg, with an outer sphere (the heaven) encompassing an inner sphere (the earth). The outer, celestial sphere contains the fixed stars as well as the sun, moon, and planets moving along its surface. The inner terrestrial sphere

846-427: A site will be high, neither misty nor frosty, and in a climate neither hot nor cold, but temperate; further, without marshes in the neighbourhood. For when the morning breezes blow toward the town at sunrise, if they bring with them mists from marshes and, mingled with the mist, the poisonous breath of the creatures of the marshes to be wafted into the bodies of the inhabitants, they will make the site unhealthy. Again, if

940-514: A wide variety of disciplines; in modern terms they would also be described as landscape architects, civil engineers, military engineers, structural engineers, surveyors, artists, and craftsmen combined. Etymologically the word architect derives from Greek words meaning 'master' and 'builder'. The first of the Ten Books deals with many subjects which are now within the scope of landscape architecture . In Book I, Chapter 1, titled The Education of

1034-552: Is a matter of conjecture, although various attempts have been made to visualise it. The early Christian practice of converting Roman basilicae (public buildings) into cathedrals implies the basilica may be incorporated into the Romanesque Fano Cathedral . In later years the emperor Augustus, through his sister Octavia Minor , sponsored Vitruvius, entitling him with what may have been a pension to guarantee financial independence. Whether De architectura

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1128-410: Is established. The topics range across many fields of expertise reflecting that in Roman times as today construction is a diverse field. Vitruvius is clearly a well-read man. In addition to providing his qualification, Vitruvius summarizes a recurring theme throughout the 10 books, a non-trivial and core contribution of his treatise beyond simply being a construction book. Vitruvius makes the point that

1222-571: Is famous for asserting in his book De architectura that a structure must exhibit the three qualities of firmitatis, utilitatis, venustatis – that is, stability, utility, and beauty. These are sometimes termed the Vitruvian virtues or the Vitruvian Triad . According to Vitruvius, architecture is an imitation of nature. As birds and bees built their nests, so humans constructed housing from natural materials, that gave them shelter against

1316-403: Is fixed in the center. Out of this arises the concept of a " celestial equator ", which is the same as the equator of the earth, projected outward onto the celestial sphere. The term " ecliptic " refers to the annual path of the sun around the celestial sphere. This path is tilted 23° with respect to the celestial equator. The two locations where the ecliptic and the celestial equator meet represent

1410-410: Is not known how he had access to this information and it is likely that knowledge of Babylonian astronomy among the successors of Hipparchus in later eras, such as Ptolemy, relied on Hipparchus for their information of it. Hipparchus' observations allowed him to discover that the tropical year was slightly less than 365.25 days, whereas the sidereal year was slightly more than 365.25 days. Hipparchus

1504-614: Is now known to have been correct, although it is not clear how Hipparchus discovered this. Claudius Ptolemy was a mathematician who worked in the city of Alexandria in Roman Egypt in the 2nd century AD, deeply examining the shape and motion of the Earth and other celestial bodies. Ptolemy's most important work was the Almagest (also known as the Mathematical Composition ) and he composed other works such as

1598-430: Is often credited as father of architectural acoustics for describing the technique of echeas placement in theaters. The only building, however, that we know Vitruvius to have worked on is one he tells us about, a basilica completed in 19 BC. It was built at Fanum Fortunae, now the modern town of Fano . The Basilica di Fano (to give the building its Italian name) has disappeared so completely that its very site

1692-520: Is sometimes given as "Marcus Vitruvius Pollio", but both the first and last names are uncertain. Marcus Cetius Faventinus writes of "Vitruvius Polio aliique auctores"; this can be read as "Vitruvius Polio, and others" or, less likely, as "Vitruvius, Polio, and others". An inscription in Verona, which names a Lucius Vitruvius Cordo , and an inscription from Thilbilis in North Africa, which names

1786-437: Is speculated that Vitruvius served with Caesar's chief engineer Lucius Cornelius Balbus . The locations where he served can be reconstructed from, for example, descriptions of the building methods of various "foreign tribes". Although he describes places throughout De Architectura , he does not say he was present. His service likely included north Africa , Hispania , Gaul (including Aquitaine ), and Pontus . To place

1880-507: Is the Naturalis Historia compiled by Pliny the Elder much later in c.  75 AD . The work is important for its descriptions of the many different machines used for engineering structures such as hoists , cranes and pulleys , as well as war machines such as catapults , ballistae , and siege engines . As a practising engineer, Vitruvius must be speaking from personal experience rather than simply describing

1974-653: Is the only source for the siege of Larignum in 56 BC. Of the battlegrounds of the Gallic War there are references to: These are all sieges of large Gallic oppida . Of the sites involved in Caesar's civil war , we find the Siege of Massilia in 49 BC (modern France), the Battle of Dyrrhachium of 48 BC (modern Albania), the Battle of Pharsalus in 48 BC (Hellas – Greece), the Battle of Zela of 47 BC (modern Turkey), and

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2068-576: The Antikythera mechanism also appears to presuppose eccentrics and epicycles in the way it produces calculations. Hipparchus was a substantial figure of Greek astronomy in the 2nd century BC. He compiled a star catalogue , according to Pliny the Elder observed a nova (new star), and discovered the precession of the equinoxes . He appears to have had substantial information about Babylonian astronomers ; no indications of such knowledge of Babylonian astronomy exists for previous Greek authors. It

2162-723: The Battle of Thapsus in 46 BC in Caesar's African campaign. A legion that fits the same sequence of locations is the Legio VI Ferrata , of which ballista would be an auxiliary unit. Mainly known for his writings, Vitruvius was himself an architect. In Roman times architecture was a broader subject than at present including the modern fields of architecture, construction management , construction engineering , chemical engineering , civil engineering, materials engineering , mechanical engineering, military engineering and urban planning ; architectural engineers consider him

2256-520: The Eupalinian aqueduct . Called "one of the greatest engineering achievements of ancient times," it is a tunnel 1,036 metres (3,399 ft) long, "excavated through Mount Kastro on the Greek island of Samos , in the 6th century BCE" during the reign of Polycrates . Scholars disagree, however, whether the dioptra was available that early. An entire book about the construction and surveying usage of

2350-594: The Hypotheses , Tetrabiblos , Handy Tables , the Canobic Inscription , and other minor works. The Almagest is one of the most influential books in the history of Western astronomy. The Almagest was a monumental series of 13 books including roughly a quarter-million words in Greek that gave a comprehensive treatment of astronomy until its time, incorporating theorems, models, and observations from many previous mathematicians. The topics covered by

2444-482: The Phaenomena of Aratus (270 BC), is the primary source for his work on this subject. The seventh and eighth books of the Almagest would constitute a star catalogue of the names, positions, and magnitudes of over a thousand stars that Ptolemy placed into the traditional classification of 48 constellations. The most important of these were the twelve constellations that defined the zodiac . Aristarchus also wrote

2538-491: The Pont du Gard . The use of the inverted siphon is described in detail, together with the problems of high pressures developed in the pipe at the base of the siphon, a practical problem with which he seems to be acquainted. He describes many different construction materials used for a wide variety of different structures, as well as such details as stucco painting. Concrete and lime receive in-depth descriptions. Vitruvius

2632-530: The Roman Forum , temples, theatres, triumphal arches and their reliefs and statues offered visual examples of the descriptions in the Vitruvian text. Printed and illustrated editions of De Architectura inspired Renaissance , Baroque and Neoclassical architecture . Filippo Brunelleschi , for example, invented a new type of hoist to lift the large stones for the dome of the cathedral in Florence and

2726-601: The Roman army under Caesar with the otherwise poorly identified Marcus Aurelius, Publius Minidius, and Gnaeus Cornelius. These names vary depending on the edition of De architectura . Publius Minidius is also written as Publius Numidicus and Publius Numidius, speculated as the same Publius Numisius inscribed on the Roman Theatre at Heraclea . As an army engineer he specialized in the construction of ballista and scorpio artillery war machines for sieges . It

2820-417: The 13 books are as follows: The Greeks sought to explain how a model could explain the irregular motions of the heavenly bodies. Since the moon and other objects appear to change in size depending on the time of observation, it was understood that the earths distance to other astral bodies was changing, and that a simple circular motion of another body around the earth, as in the homocentric theory of Eudoxus,

2914-540: The 5th and 4th centuries BC, and Hellenistic Astronomy , which encompasses the subsequent period until the formation of the Roman Empire ca. 30 BC, and finally Greco-Roman astronomy , which refers to the continuation of the tradition of Greek astronomy in the Roman world. During the Hellenistic era and onwards, Greek astronomy expanded beyond the geographic region of Greece as the Greek language had become

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3008-932: The 6th century, the Romaka Siddhanta ("Doctrine of the Romans"), and the Paulisa Siddhanta (sometimes attributed as the "Doctrine of Paul " or in general the Doctrine of Paulisa muni) were considered as two of the five main astrological treatises, which were compiled by Varahamihira in his Pañca-siddhāntikā ("Five Treatises"). In addition to the authors named in the article, the following list of people who worked on mathematical astronomy or cosmology may be of interest. Vitruvius Vitruvius ( / v ɪ ˈ t r uː v i ə s / vi- TROO -vee-əs , Latin: [wɪˈtruːwi.ʊs] ; c.  80 –70 BC – after c.  15 BC )

3102-484: The Almagest as opposed to improving or building upon it. This changed in the fifth century with the Neoplatonist philosopher Proclus . His exposition of the Almagest displayed, unlike his predecessors, a detailed grasp of the technical details of Ptolemy's work. Though Proclus criticized some elements of the Almagest, such as its suggestion of the existence of epicycles, he and future Neoplatonists believed astronomy

3196-456: The Architect, Vitruvius instructs... 1. Architecture is a science arising out of many other sciences, and adorned with much and varied learning; by the help of which a judgment is formed of those works which are the result of other arts. Practice and theory are its parents. Practice is the frequent and continued contemplation of the mode of executing any given work, or of the mere operation of

3290-476: The Elder and Vitruvius contain some information on Greek astronomy. The most important primary source is the Almagest , since Ptolemy refers to the work of many of his predecessors. The main features of Archaic Greek cosmology are shared with those found in ancient near eastern cosmology . They include (a flat ) earth, a heaven (firmament) where the sun, moon, and stars are located, an outer ocean surrounding

3384-466: The Eudoxan theory of homocentrics, since it did not allow for any variation in the distance between the earth and the moon. Apollonius of Perga ( c.  240 BCE  – c.  190 BCE ) responded to the problems in earlier astronomical theories, especially that of Eudoxus, by producing the theory of eccentrics and epicycles (and their deferents). This was further elaborated on by Hipparchus in

3478-607: The Florentine humanist Poggio Bracciolini in the library of Saint Gall Abbey . Leon Battista Alberti published it in his seminal treatise on architecture, De re aedificatoria ( c.  1450 ). The first known Latin printed edition was by Fra Giovanni Sulpitius in Rome in 1486. Translations followed in Italian, French, English, German, Spanish, and several other languages. Though any original illustrations have been lost,

3572-532: The Greek term πλανήτης ( planētēs ), meaning "wanderer", as ancient astronomers noted how certain points of lights moved across the sky in relation to the other stars (which appear fixed). Five planets can be seen with the naked eye: Mercury , Venus , Mars , Jupiter , and Saturn , the Greek names being Hermes, Aphrodite, Ares, Zeus and Cronus. Early Greek astronomers thought that the evening and morning appearances of Venus represented two different objects, calling it Hesperus ("evening star") when it appeared in

3666-706: The Greeks") was translated from Greek to Sanskrit by Yavanesvara during the 2nd century, under the patronage of the Western Satrap Saka king Rudradaman I . Rudradaman's capital at Ujjain "became the Greenwich of Indian astronomers and the Arin of the Arabic and Latin astronomical treatises; for it was he and his successors who encouraged the introduction of Greek horoscopy and astronomy into India." Later in

3760-490: The calendar and the parapegma literature. Eudoxus' model of planetary motion survives as summarized by Aristotle ( Metaphysics XII, 8) as well as the commentary of Simplicius on the De caelo of Aristotle, produced in the 6th century AD. Eudoxus' model attempted to explain the planetary motions being observed. The key means by which it did so was by saying the fixed stars were moved along one rotating sphere, whereas each of

3854-454: The care of furnishing the troops with wood and straw, as well as the rams, onagri , balistae and all the other engines of war under his direction. This post was always conferred on an officer of great skill, experience and long service, and who consequently was capable of instructing others in those branches of the profession in which he had distinguished himself. At various locations described by Vitruvius, battles and sieges occurred. He

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3948-482: The construction of sundials and water clocks ; and the design and use of machines in construction and warfare. He further divides building into public and private. Public building includes city planning, public security structures such as walls, gates and towers; the convenient placing of public facilities such as theatres, forums and markets, baths, roads and pavings; and the construction and position of shrines and temples for religious use. Later books are devoted to

4042-426: The cosmic order). In this book series, Vitruvius also wrote about climate in relation to housing architecture and how to choose locations for cities. Vitruvius is the first Roman architect to have written surviving records of his field. He himself cites older but less complete works. He was less an original thinker or creative intellect than a codifier of existing architectural practice. Roman architects practised

4136-403: The cosmos. Like his predecessors, such as Hesiod and Homer , he believed the Earth to have been flat and resting on a primordial and endless ocean. However, he proposed that the universe was fundamentally composed of water. The most famous successors of the tradition begun by Thales were Plato and Aristotle ; while much thought continued to rely on intuition, the lasting legacy of this work

4230-428: The dioptra is credited to Hero of Alexandria (also known as Heron; a brief description of the book is available online; see Lahanas link, below). Hero was "one of history’s most ingenious engineers and applied mathematicians ." The dioptra was used extensively on aqueduct building projects. Screw turns on several different parts of the instrument made it easy to calibrate for very precise measurements The dioptra

4324-442: The elements. When perfecting this art of building, the Greeks invented the architectural orders: Doric , Ionic and Corinthian . It gave them a sense of proportion, culminating in understanding the proportions of the greatest work of art: the human body. This led Vitruvius in defining his Vitruvian Man , as drawn later by Leonardo da Vinci : the human body inscribed in the circle and the square (the fundamental geometric patterns of

4418-406: The equinoxes (in the spring and fall ). The two points where the ecliptic is furthest away from the equator represents the solstices ( summer and winter ). Eudoxus of Cnidus lived and practiced astronomy in the first half of the fourth century BC. His works are lost and so information about him comes from secondary references in ancient texts. There is a group of fragments about astronomy in

4512-465: The first half of the fourth century BC, and with them came a decisive shift in Greek astronomy. The work of these two figures represents a shift from earlier stellar concerns, focusing on the study of the stars, to the study of the planet. A new two-sphere model of the solar system was proposed, and, for the first time, explanations for planetary observations were posited in the form of geometric theories. The two-sphere model posits that heaven and earth are

4606-575: The first illustrated edition was published in Venice in 1511 by Fra Giovanni Giocondo , with woodcut illustrations based on descriptions in the text. Bramante , Michelangelo , Palladio , Vignola and earlier architects are known to have studied the work of Vitruvius, and consequently it has had a significant impact on the architecture of many European countries. Little is known about Vitruvius' life. Most inferences about him are extracted from his only surviving work De Architectura . His full name

4700-426: The first illustrated edition was published in Venice in 1511 by Fra Giovanni Giocondo , with woodcut illustrations based on descriptions in the text. Later in the 16th-century Andrea Palladio provided illustrations for Daniele Barbaro 's commentary on Vitruvius, published in Italian and Latin versions. The most famous illustration is probably Da Vinci's Vitruvian Man . The surviving ruins of Roman antiquity,

4794-406: The first of their discipline, a specialization previously known as technical architecture. In his work describing the construction of military installations, he also commented on the miasma theory – the idea that unhealthy air from wetlands was the cause of illness, saying: For fortified towns the following general principles are to be observed. First comes the choice of a very healthy site. Such

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4888-465: The fourth century BC known as the Eudoxus Papyrus , but it contains little relevant informations about the views of Eudoxus himself. According to Hipparchus in his commentary on Aratus , Eudoxus is thought to have written include one called Mirror and another called Phaenomena , though an Oktaeteris is pseudonymously attributed to him. Another work, On Speeds , endeavored to understand

4982-405: The hands, for the conversion of the material in the best and readiest way. Theory is the result of that reasoning which demonstrates and explains that the material wrought has been so converted as to answer the end proposed. 2. Wherefore the mere practical architect is not able to assign sufficient reasons for the forms he adopts; and the theoretic architect also fails, grasping the shadow instead of

5076-465: The human body led to the famous Renaissance drawing of the Vitruvian Man by Leonardo da Vinci . Little is known about Vitruvius' life, but by his own description he served as an artilleryman, the third class of arms in the Roman military offices. He probably served as a senior officer of artillery in charge of doctores ballistarum (artillery experts) and libratores who actually operated

5170-409: The human body, and by extension, of the universe as a whole. In the introduction to book seven, Vitruvius goes to great lengths to present why he is qualified to write De Architectura . This is the only location in the work where Vitruvius specifically addresses his personal breadth of knowledge. Similar to a modern reference section, the author's position as one who is knowledgeable and educated

5264-463: The inhabited human realm, and the netherworld ( Tartarus ), the first three of which corresponded to the gods Ouranos , Gaia , and Oceanus (or Pontos ). The philosopher Thales , one of the primary figures of the Ionian school of Greek philosophy is usually credited for initiating the tradition of Greek science . Thales was the first to offer a non-mythological explanation for the composition of

5358-543: The language of scholarship throughout the Hellenistic world, in large part delimited by the boundaries of the Macedonian Empire established by Alexander the Great . The most prominent and influential practitioner of Greek astronomy was Ptolemy , whose treatise Almagest shaped astronomical thinking until the modern era. Most of the most prominent constellations known today are taken from Greek astronomy, albeit via

5452-438: The larger circle rotating around the earth, and this smaller circle is called a deferent. The body itself rotates around the circle of the deferent, meanwhile the deferent as a whole would be rotating around the earth. This would also enable an observer from the earth to observe an irregular motion on the part of the astral body. Eccentrics and epicycles are the two main tools of Ptolemaic astronomy, and Ptolemy demonstrated that

5546-410: The late 1st century AD to administer the many aqueducts of Rome), writing a century later, gives much more detail of the practical problems involved in their construction and maintenance. Surely Vitruvius' book would have been of great assistance in this. Vitruvius was writing in the 1st century BC when many of the finest Roman aqueducts were built, and survive to this day, such as those at Segovia and

5640-477: The machines. As an army engineer he specialized in the construction of ballista and scorpio artillery war machines for sieges . It is possible that Vitruvius served with Julius Caesar 's chief engineer Lucius Cornelius Balbus . Vitruvius' De architectura was well-known and widely copied in the Middle Ages and survives in many dozens of manuscripts, though in 1414 it was "rediscovered" by

5734-400: The moon was passing by closer to the earth, its motion would seem faster and it would look larger (because it was closer); otherwise, it would appear slower and smaller. The notion of an epicycle was to say that there was a circle of rotation around the earth, but to reject the idea that the rotating body itself would be placed on that circle. Instead, a smaller rotating circle would be placed on

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5828-517: The northern sky seems to turn around the North star , which led him to the concept of a Celestial sphere around Earth. And, as the sky seems to vary with latitude, he also considered that Earth's surface may be curved as well. However, he incorrectly thought that the Earth was a cylinder as opposed to a sphere. The notion of a spherical Earth first found an audience with the Pythagoreans , but this

5922-441: The planets moved along several nested rotated spheres each with their own speed and pole. Eudoxus established a school of thought that prioritized the use of geometrical models to explain the apparent paths of the stars. Some, however, noticed flaws in the system of Eudoxus. Autolycus of Pitane observed that the moon would be observed to be a different size when the observation was taken at different times. However, this contradicted

6016-505: The planets revolved around it, was dominant in ancient Greece and ancient cosmographical systems more generally. However, various alternatives appeared at one time or another. For example, the Pythagorean astronomical system , as proposed by Philolaus in the 5th century BC, proposed that there was an unseen "Central Fire" (not to be confused with the sun) around which all other bodies of the cosmos revolved. Heraclides Ponticus posited

6110-704: The preface of Book I, Vitruvius dedicates his writings to giving personal knowledge of the quality of buildings to the emperor. Likely Vitruvius is referring to Marcus Agrippa 's campaign of public repairs and improvements. This work is the only surviving major book on architecture from classical antiquity . According to Petri Liukkonen, this text "influenced deeply from the Early Renaissance onwards artists, thinkers, and architects, among them Leon Battista Alberti (1404–1472), Leonardo da Vinci (1452–1519), and Michelangelo (1475–1564)." The next major book on architecture, Alberti's reformulation of Ten Books ,

6204-477: The role of Vitruvius the military engineer in context, a description of "The Prefect of the camp" or army engineer is quoted here as given by Flavius Vegetius Renatus in The Military Institutions of the Romans : The Prefect of the camp, though inferior in rank to the [Prefect], had a post of no small importance. The position of the camp, the direction of the entrenchments, the inspection of

6298-411: The second century BC and, later, by Ptolemy in the 2nd century AD. This model allowed for theory to account for changes in the distance between the earth and other astral bodies. However, while Apollonius is often credited with developing this theory, some think that the evidence for this is tenuous. Some evidence may tie in an earlier author, Archimedes , with knowledge of epicycles and eccentrics, and

6392-461: The substance. He who is theoretic as well as practical, is therefore doubly armed; able not only to prove the propriety of his design, but equally so to carry it into execution. He goes on to say that the architect should be versed in drawing, geometry, optics (lighting), history, philosophy, music, theatre, medicine, and law. In Book I, Chapter 3 ( The Departments of Architecture ), Vitruvius divides architecture into three branches, namely; building;

6486-418: The tents or huts of the soldiers and the baggage were comprehended in his province. His authority extended over the sick, and the physicians who had the care of them; and he regulated the expenses relative thereto. He had the charge of providing carriages, bathhouses and the proper tools for sawing and cutting wood, digging trenches, raising parapets, sinking wells and bringing water into the camp. He likewise had

6580-564: The terminology they took on in Latin . Greek astronomy was heavily influenced by Babylonian astronomy and, to a lesser extent, Egyptian astronomy. In later periods, ancient Greek astronomical works were translated and promulgated in other languages, most notably in Arabic by the astronomers and mathematicians within the various Arab-Muslim empires of the Middle Ages . Many Greek astronomical texts are known only by name, and perhaps by

6674-436: The text in later centuries that further engage with the Almagest. The author of the original commentary is, however, not known, as many plausible candidates studied in the astronomy of Ptolemy lived in this era, such as Eutocius of Ascalon and John Philoponus . Several Greco-Roman astrological treatises are also known to have been imported into India during the first few centuries of our era. The Yavanajataka ("Sayings of

6768-513: The then-unpredictable motions of the planets. He began his work in Athens and Egypt , he went on to found a school in Cyzicus where he gained his reputation. His pupils include Menaechmus , credited as the inventor of the notion of conic sections, and Polemarchus , whose own pupil Callippus offered well-received modifications of the Eudoxan theory of homocentric spheres. He also contributed to

6862-414: The town is on the coast with southern or western exposure, it will not be healthy, because in summer the southern sky grows hot at sunrise and is fiery at noon, while a western exposure grows warm after sunrise, is hot at noon, and at evening all aglow. Frontinus mentions Vitruvius in connection with the standard sizes of pipes : probably the role for which he was most widely respected in Roman times. He

6956-407: The true figure of 40,120 kilometers. Hipparchus wrote another book On the Sizes and Distances of the Sun and Moon , which has not survived. Both Aristarchus and Hipparchus drastically underestimated the distance of the Sun from the Earth. Geocentrism , the idea that the Earth was at the center of the solar system (or even cosmos) and that the other heavenly bodies, including the sun, moon, and

7050-450: The two were closely related. In the case of the sun, Ptolemy understood that its motion could be predicted either by an eccentric or by an epicycle. Once celestial bodies other than the sun were introduced to the model, such as the planets, it became more complex. The models for Jupiter, Saturn, and Mars included the center of the circle, the equant point, the epicycle, and an observer from earth to give perspective. The discovery of this model

7144-406: The understanding, design and construction of each of these. In Book III, Chapter 1, Paragraph 3, Vitruvius writes about the proportions of man: 3. Just so the parts of Temples should correspond with each other, and with the whole. The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre,

7238-562: The universe with the Moon, the Sun, and five planets circling it. The circle of fixed stars marked the outermost sphere of the universe and beyond that would be the philosophical "aether" realm. The Earth was at the exact center of the cosmos. The sphere carrying the Moon is described as the boundary between the corruptible and changing sublunary world and the incorruptible and unchanging heavens above it. Ptolemaic astronomy became standard in medieval western European and Islamic astronomy until it

7332-405: The western evening sky and Phosphorus ("light-bringer") when it appeared in the eastern morning sky. They eventually came to recognize that both objects were the same planet. Credit is variously attributed to Pythagoras or Parmenides for this discovery. Eudoxus is typically thought to have standardized the names of the constellations. The earliest extant description of the constellations,

7426-698: The work of some of the most talented is unknown, while many of those of lesser talent but greater political position are famous. This theme runs through Vitruvius's ten books repeatedly – echoing an implicit prediction that he and his works will also be forgotten. Vitruvius illustrates this point by naming what he considers the most talented individuals in history. Implicitly challenging the reader that they have never heard of some of these people, Vitruvius goes on and predicts that some of these individuals will be forgotten and their works lost , while other, less deserving political characters of history will be forever remembered with pageantry. Vitruvius' De architectura

7520-404: The works of others. He also describes the construction of sundials and water clocks , and the use of an aeolipile (the first steam engine ) as an experiment to demonstrate the nature of atmospheric air movements (wind). His description of aqueduct construction includes the way they are surveyed, and the careful choice of materials needed, although Frontinus (a general who was appointed in

7614-555: Was "rediscovered" in 1414 by the Florentine humanist Poggio Bracciolini in the library of Saint Gall Abbey . Leon Battista Alberti (1404–1472) publicised it in his seminal treatise on architecture, De re aedificatoria ( c.  1450 ). The first known Latin printed edition was by Fra Giovanni Sulpitius in Rome, 1486. Translations followed in Italian ( Cesare Cesariano , 1521), French (Jean Martin, 1547 ), English, German ( Walther H. Ryff , 1543) and Spanish and several other languages. The original illustrations had been lost and

7708-766: Was a Roman architect and engineer during the 1st century BC, known for his multi-volume work titled De architectura . As the only treatise on architecture to survive from antiquity, it has been regarded since the Renaissance as the first book on architectural theory , as well as a major source on the canon of classical architecture . It is not clear to what extent his contemporaries regarded his book as original or important. He states that all buildings should have three attributes: firmitas , utilitas , and venustas ("strength", "utility", and "beauty"), principles reflected in much Ancient Roman architecture . His discussion of perfect proportion in architecture and

7802-588: Was clear that he had set down his own discoveries. James Anderson's "The Constitutions of the Free-Masons" (1734), reprinted by Benjamin Franklin, describes Vitruvius as "the Father of all true Architects to this Day." Vitruvius is the author of De architectura, libri decem , known today as The Ten Books on Architecture , a treatise written in Latin on architecture, dedicated to the emperor Augustus. In

7896-416: Was displaced by Maraghan , heliocentric and Tychonic systems by the 16th century. The first critical discussion of the Almagest is by Artemidorus in the late second or early third century, though he understood it poorly. In the fourth century, Pappus of Alexandria and Theon of Alexandria composed commentaries or treatises on sections of the Almagest. These works, however, only sought to understand

7990-496: Was due to philosophical as opposed to scientific reasons: the sphere was considered a perfectly geometrical figure. According to Ptolemy in his Almagest (1.2), Greek astronomy was predicated on the following assumptions (or hypotheses in Greek terminology): The first book of the Almagest included a chapter dedicated to the defense of each of these assumptions and refuting alternative positions, using both philosophy and astronomical observation. The term "planet" comes from

8084-408: Was essential to theology and continued to read Ptolemy's works. Students and successors of Proclus to continue working in the tradition of the Almagest included Hilarius of Antioch and Marinus. An ill-studied full-scale commentary on the Almagest was produced in the sixth century, and of interest to historians are the significant number of scholia to its margins and between columns by scribes copying

8178-650: Was inspired by De Architectura as well as surviving Roman monuments such as the Pantheon and the Baths of Diocletian . Latin Italian French English Books VIII, IX and X form the basis of much of what we know about Roman technology, now augmented by archaeological studies of extant remains, such as the water mills at Barbegal in France. The other major source of information

8272-480: Was not written until 1452. However, we know there was a significant body of writing about architecture in Greek, where "architects habitually wrote books about their work", including two we know of about the Parthenon alone. To A. W. Lawrence , Vitruvius "has recorded a most elaborate set of rules taken from Greek authors, who must have compiled them gradually in the course of the preceding centuries". Vitruvius

8366-543: Was replaced as a surveying instrument by the theodolite . Greek astronomy Ancient Greek astronomy is the astronomy written in the Greek language during classical antiquity . Greek astronomy is understood to include the Ancient Greek , Hellenistic , Greco-Roman , and late antique eras. Ancient Greek astronomy can be divided into three primary phases: Classical Greek Astronomy , which encompassed

8460-414: Was that it offered non-supernatural explanations for the normal operations of the universe; mathematics (especially geometry ) was significantly developed and applied on the problems that were worked on; and it was thought that observation could disqualify candidate explanations for how the world worked. Anaximander , a student of Thales and another prominent member of the Ionian school, realized that

8554-524: Was that the center of the Mercury and Venus epicycles must always be colinear with the Sun. This assures of bounded elongation. Bounded elongation is the angular distance of celestial bodies from the center of the universe. Ptolemy's model of the cosmos and his studies landed him an important place in history in the development of modern-day science. In the Ptolemaic system, the Earth was at the center of

8648-404: Was unable to account for this. Ptolemy accepted and elaborated on the notion of eccentrics and epicycles to explain this phenomenon. The eccentric is the posit that the observer is not located at the center of rotation. Therefore, if the earth were not, for example, at the center of the rotation of the earth, the moon would appear to have a nonuniform motion to an observation from the earth: when

8742-417: Was upon these writings that Renaissance engineers, architects and artists like Mariano di Jacopo Taccola , Pellegrino Prisciani and Francesco di Giorgio Martini and finally Leonardo da Vinci based the illustration of the Vitruvian Man . Vitruvius described the human figure as being the principal source of proportion. The drawing itself is often used as an implied symbol of the essential symmetry of

8836-463: Was written by one author or is a compilation completed by subsequent librarians and copyists, remains an open question. The date of his death is unknown, which suggests that he had enjoyed only a little popularity during his lifetime. Gerolamo Cardano , in his 1552 book De subtilitate rerum , ranks Vitruvius as one of the 12 persons whom he supposes to have excelled all men in the force of genius and invention; and might have given him first place if it

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