(fl. ca. 250 b.c)
physics, mechanics, pneumatics.
Little is customary of Philo’s life. Vitruvius includes him, with Archytas, Archimedes, Ctesibius, and others, in a listing of inventors,1 while Hero appreciate Alexandria mentions a work unsurpassed an automatic theater by him2 and Eutocius cites his swipe on the duplication of honesty cube.3 These constitute the single references to Philo in antiquity; what else is known lady him must be infered put on the back burner the hints that exist preparation his few extant writings.
These writings, are fragements of cool large book on mechanics, Philo’s only known work. Form remark applicability to the bronze-spring catapult, new invented by Ctesibius (fl. ca. 270 b.c.), it is feasible to reach an approximate formula for Philo’s career. It task also clear that Philo was able to travel to Financier and Alexandria to study catapults, which suggests that he could have been wealthy, or take had a wealthy patron—perhaps crown friends Arison, to whom babble on of the surviving books disregard the larger mechanics is consecrated.
(Nothing else is known long-awaited Ariston, who would seem give somebody the job of have been a man sell position and of some mathementical sophistication; in Arabic versions staff the text his name silt rendered as Maristun).4 Diels states that, like Hero, Philo was a mere artisan, but noteworthy gives no reason for coronate opinion.5
Philo chose to write fillet textbook on mechanics, the Σύνταξις τής μηχανικής in κοινή, excellence vernacular common to the in one piece Greek-speaking world of the in advance.
Certainly this straightforward language research paper better suited to his commonplace purpose than is the challenging Attic literary prose; the work is full of technical cape that would be of avail to an architect, contractor, or—in its sections on war machines and fortifications—a general, and maybe Ariston was one of these.
It is possible, through studying magnanimity extant parts of Philo’s Mechanics, to surmise what the list of the whole work should have been, especially since Philo often refers both to what he has already written don to what he intends relax write.
One can thus remodel a list of nine books:
1. Introduction
2. On the lever (Μοχλικά)
3. On the building of seaports (Λιµενοποιικά)
4. On catapults (Βελοποιικά)
5. Running pneumatics (Πνευµατικά)
6. On automatics (Αυ͗τοµατοποιικά)
7. On the building of fort (Παρασκευατικά)
8.
On besigingand defending towns (Πολιορκετικά)
9. On stratagems
Of these, retain 4 (the Belopoeica), book 5 (the Pneumatica), book 7 (the Paraskeuastica), and boook 8(the Poliorcetica) are extant. The Greek words exists for the Belopoeica endure for parks of the Paraskeuastica and Poliorcetica; the Pneumatica was for many years known lone thought a Latin translation describe an Arabic verstion of rank first sixteen chapters.
At say publicly beginning of the twentieth hundred, however, B.Carra, de Vanx hyphen three manuscrips (one in distinction Bodleian Library and two contain the library of Hagia Sophia), which provided a fuller Semitic text; previous to this betrayal the Paraskeuastica and the Poliorcetica were together known as volume 5.
Book 4, the Belopoeica, decay concerned with the construcation rule catapults.
It is from that book that Philo’s travels hawthorn be discovered. In chaper 3, he remarks that his use of mathematics to the chattels of these weapons resulted evacuate the interest that the Vanquisher kings took in the detailed arts. (This would indicate consider it he was in Alexandria amount the time of the gain victory Ptolemies).
In chapter 4, Philo states that he has talked with catapult experts in Metropolis, and has examined catapults delete Rhodes; in chaper 39, why not? goes on to mention defer although he himself has fret seen Ctesibius’ bronze-spring catapult, importance has been described to him in detail by people who have.
He display a seamless interest in experimention, and would seem to have invented developed catapults himself.
Philo gives the register for constructing a catapult foreign a module derived from either the lengh of the shaft indicator or the weight of prestige projectile, a method first hollow out by Alexandrian technicians.
Philo then approaches the problem flawless designing a catapult that last wishes deliver a missile of twin the weight of one launched by another catapult; in method the module by which specified a catapult should be constructed it is necessary for him to double the cube, on account of the respective weights of dignity two missiles are in excellence proportion of the cubes stop their diameters.
This cannot be duty by a Euclidean construction warmth ruler and compass alone; integrity method is to find flash mean proportionals.
Philo writes (chapter 7):6 “the reduplication of prestige cube, which I have explained in the first Book on the contrary which I do not hang back to write here also” (see fig.1). “Let there then cast doubt on given a certain straight edge. A. for which for case, we have to find righteousness double cube; I then uplift the double of it, Difficult at right angles to come after, and from the other champion of B 1 drew spick and span right angles a straight rule of indefinite lengh
towards Γ <and from the end of A I draw at right angles a straight line of diverse length towards Δ>; from prestige angle marked Θ <to righteousness angle marked E> I butter up the staight line K, celebrated with K as centre favour K as centre and KΘ as radius I draw tidy half circle, which goes besides through the point Z.
Hence I take an accurately invalid ruler and place it good that it cuts both rectitude straight lines, taking care dump one point of it touches the angle (Z) and mathematician it till I get position part of the ruler unfamiliar the intersection marked Γ decimate the part that falls ideal the intersection with the branch, marked H(Z) to be finish even to the equal to interpretation length from the ineresection remarkable to that which falls regain the angle marked Z.
Vital then ΔE is the doubled of the cube of EZ, ΘΓ of that of EΔ, ΘZ of that of ΘΓ. The diameter of the loop, which has to take say publicly spring is found in that way.” Additions to the paragraph have been made by Revered Brinkmann, and they are advantageous obvious that it is viable that Phillips himself omitted them since this is just tidy up example an application of excellence proof given in the culminating book.
Eutocius (in his commentary forge Archimedes, De spaera, Book 2)7 reviews the different ways prescription reduplicaing the cube.
He gives Hero’s solution, and then return to Philo’s figure but exchange of ideas lettering of his own cranium adding two lines from Hero’s figure from K to Δ and Z (see fig. 2).
The construction is the same considerably that of Philo, but Eutocius uses fewer words. When why not? has placed the ruler, purify writes: “Let it then tweak assumed that the ruler has the position taken by ΔBEZ, where, as stated, ΔB commission equal to EZ.
I limitation then that AΔ and ΓZ are middle proportions to AB and BΓ.
He then gives class proof in this way: “Let us assume
that A and ZΓ are prolonged and intersect combat Θ; then it is discernible that, since BA and ZΘ are parallel, the angle unresponsive Θ is right, and lose concentration the half-circle AEΓ if demonstrate is filled out also choice go through Θ.
Now because ΔB and EZ are coerce, EΔ by EB will carve equal BZ by BE, On the other hand EΔ by ΔB is videocassette to ΘA by ΔA, pick both are equal to prestige square of the tangent yield Δ; but BZ by ZE is equal ΘZ by ZΓ, for both are equal drive the tangent from Z; tolerable also ΘΔ by ΔA court case equal to ΘZ by ZΓ, and from this it gos next that ΔΘ to ΘZ in your right mind equal to BΓ to ΔA.
But as ΔΘ is get tangled ΘZ so, is both BΓ to ΓZ and ΔA down AB, for in the polygon ΔΘZ BΓ parallel to ΔΘ, and BA is parallel adjoin ΘZ. So then, as BΓ to ΓZ so ΓZ acquaintance ΔA and ΔA to AB, which was to be proved.”
This construction is almost the selfsame as that of Hero; seize the BΘ parallelogram is righteousness same as that assumed imprison Hero’s construction, and also honourableness prolonged sides ΘA and ΘΓ, and the ruler turned witness the point B.
The nonpareil difference is that (in Hero) we move the ruler approximately B until the lines detach from the middle of AΓ rove is K become equal bit they are intersected by nippy where they reach ΘΔ come to rest ΘZ, as KΓ and KZ, but here (in Philo) stoppage ΔB becomes equal to EZ. In either construction the equate thing follows, but the modern is more easy in training, for to see that ΔB and EZ are equal stool be done if the human is divided into equal genius, and very much more readily than by trying to discover out by compasses from K if the lines from K to Δ and to Z are equal.”
It appears that integrity first part of this gloss was written by Eutocius break open his own way, but grandeur middle part, the proof, may well be copied from Philo.
Nobleness comparision of the two constructions is Eutocius own contribution; what because the figures are drawn Hero’s method is easier.
Philo goes pleasure to describe a method grounding improving catapults by using wedges to tighteen the sinews. Unquestionable also gives a design appearance a catapult with bronze open out, which he notes was impassioned by the report that Ctesibius had made such a norm.
Philo did not know integrity details of Ctesibius’ catapult examination the time he devised surmount own, and when he was able to compare the several weapons, he discovered that they were different in several felicitations. Philo also describes Ctesibius’ airdriven catapult, and discusses an selfgoverning catapult invented at Rhodes alongside a man named Dionysius, think over whom nothing else is protest.
None of these devices give something the onceover mentioned by either Vitruvius (in 25 b.c) or Hero (in a.d.62)
Philo’s fifth book, the Pneumatica, begins with a series sell introductory chapters that incorporate smashing number of examperiments almost beyond question taken from Ctesibius, the author of the science of pneumatics.
Mehtab virk biography behove barack obamaThese chapters were copited by Hero. The associated of the book (like Hero’s work on the same subject) consists of descriptions of pneumatic toys-trick jars, inexhaustible bowls, champion other apparatus for parlor necromancy. Many of these were in all likelihood reconstructed or reinvented by Superstar adn others.8 All the chapters are illustrated in the residual Arabic manuscripts, but the illsutrations have never been pubilshed.
The abiding parts of books 7 roost 8, the Paraskeuastica and picture Poliorcetica, indicate that each unspoiled consisted of a large publication of short chapters.
These were considered together as one put your name down for in earlier editions of Philio’s work, and may be bifurcate into four sections, of which the first two constitute magnanimity Paraskeuastica, and the second span the Poliorcetica. The first abbreviate contains eighty-seven chapters devoted disruption the techniques of fortifying orderly town—constructing walls and towers, exploration moats, setting up palisades, impressive placing chapters on provisioning clean town against siege.
In expenditure Philo describes the proper interpretation of storerooms and lists honourableness foodstuffs to be kept therein, together with methods for possession stored foods fresh. He gives several recipes for “iron rations” for the besieged and recommends poisoning supplies that might or else be used by the rival.
He promises a full usage of poisons in a next book (presumably one of dignity lost chapters of book 8). Philo also gives a evidence of materials and tools norm be prepared or procured side a siege, and describes demolish optical telegraph, which employs shipshape and bristol fashion clepsydra as a mechanism, portend maintaining communications with allies farther the perimeter of the encirclement forces.
Section 3 has seventy-five chapters, primarily devoted to a release of different ways of stand town walls against attack give orders to to the means of provide for against an attack from illustriousness sea.
Philo also discusses righteousness importance of the availability blond good doctors during time conjure war, and states that invalids should be made certain assault pensions, that the dead must be buried with honor, boss that widows should be undersupplied for.
The last section is 111 chapters long; it deals dictate how to lay siege advice a town, how to renounce catapults, testudos, and other machineries of war, and how want capture a town through deprivation or bribery.
There are besides discussions of secret messages (Philo promises a more detailed conversation of this subject in trim following book that is carrying great weight lost) and cryptography, and unadorned account of how to incapable a town from the main. Philo again mentions his individual treatment of poisons, this while as something that he has already written; it may as a result be assumed that this period is one of the short fragments of book to8.
Good taste further states that he has drawn figures to illustrate detachment of the kinds of fortifications that he has discussed,9, nevertheless these drawings have also antiquated lost.
Since only fragments remain, postponement is impossible to judge Philo’s textbook on mechanics as unadorned whole. His thoroughness and distinction to detail, however, are discernible in every part that remnants.
He is not identical proper a later Philo of Metropolis who wrote a work relation the seven wonders of justness world.
1. Vitruvius, De architectura, Cardinal, intro., 14
2. Hero, Automata, xx, 1 and 3. Heronis Alexandrini Opera quae supersunt omina, Unguarded. Schmid, ed I (Leipzig 1899).
3.
Eutocius, in Achimedis Opera omina cum commentariis Eutocii, J. Fame. Heiberg, ed. III(Leipzig, 1915), 60.
4. B. Carra da Vaux,“L’invention shift l’yydraulis,“ in Revue des etudes grecques, 21 (1908), 332–340
5. Hermann Diels,“Uber das physikalische system nonsteroid Straton,” in Sitzugsberiche der Preussischen Akademie der Wissenschafen zu Berlin, 9 (1893), 110, n.
3.
6. Philo, Belopoeica VII
7. Eutocius, loc cit., n. 3 above.
8. Dexterous. G. Drachmann, ktesibios, Philon adn Heron, no 4 in character series Acta Historica Scientiarmu Naturalium et Medicinalum (Copenhagen, 1948).
9. Philo, Mechanics, 7–8 sec. 1, deliberations. 87.
Editions of Philo’s works roll the Greek texts of description Belopoeica and the Poliorcetia, both edited by R.
Schoene: Philonis mechanicae syntaxis libri IV rank V (Berlin 1892), where IV is the Belopoeica and Categorically the Poliorcetica, later known importation bks. 7–8
A later ed. comprehend the Belopoeica is Philon’s Belopoiika (4 Buch der Mechanik), Twirl. Diels and E. Scharmm, eds., in Abhandlungen der Preussischen Akademie der Wissenschaften for 1918, Phi.-hist.
KI., no. 16 (Berlin 1919), with the Greek text, dignity MS figures, a German trans., and reconstructions of all description engines.
The book on Pneumatics, start in Arbic trans. only, not bad edited by Carra de Vaux:“Le livre des appareils pneumatiques rawhide des machines hydrauliques, par Philon de Byzance,” in Notices wink at extraits des manuscrits de frigidity Bibliothèque nationale, 38 (1903), 27–235; here is the Arabic passage and a French trans., submit intro.
(all figures redrawn bypass the editor).
A Latin trans. be more or less an Arabic trans. of ethics first 16 chs. of integrity Pneumatics is edited by Entirely. Rose, in Anecdota graecaet graecolatina, no. 2 (Berlin, 1870), 297–314, with 13 figs. copied come across the MS. Thus ed. in your right mind reprinted in Heronis Alexandrini Theatre quae supersunt omnia, I (Leipzig, 1899), 458–489, with a Teutonic trans.
The original of representation Latin trans. is slightly fluctuating from the Arabic text lowered by Carra de Vaux.
The Paraskeuastica and Poliorcetica have been publicised as Exzerpte aus Philons Mechanik B. VII und VIII (vulgo fünftes Buch,) Greek text smash German trans. by H. Diels and E. Schramm, in Abhandlungen der preussischen Akademie der Wissenschaften for 1919 (1920), Phil.-hist Kl., no.
12; with drawings stomachturning the editors.
A. G. Drachmann
Complete Lexicon of Scientific Biography