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WORK I:<br>APOLLONII // PERGAEI CONICORVM // LIBRI QUATTVOR.// VNA CVM PAPPI ALEXANDRINI // LEMMATIBVS ET COMMENTARIIS // EVTOCII ASCALONITAE. // SERENI ANTINSENSIS // PHILOSOPHI LIBRI DUO // NVNC PRIMVM IN LVCEM EDITI. // QVAE OMNIA NVPER FEDERICVS // Commandinus Vrbinas mendis quamplurimis expur-// gata è Graeco conuertit & commen- // tariis illustrauit. // CVM PROVILEGIO PII IIII. PONT. MAX. // IN ANNOS X.// BONONIAE // EX OFFICINA ALEXANDRI BENATII. // M D L X VI. <br>

1566 · B6630 — Bononiae /Bologna: Alexandri or Alexander or Alessandro Benatii or Benatius or Benacci publisher c. 1566. . Edition: First Commandino edition. Binding: 17th century mottled calf; spine raised with six 6 bands compartments gilt gilt lettered title on two; all edges speckled red. Notes: First edition by Commandino. David Clement judges this edition of the first four books bound with the two books of Sereni on cones and cylinders to be extremely rare. Also footnote 32 states: in Bibliotheca Uilenbroukiana P.I. p. 55. Catal. duarum Bibliothecaruin Dom. N. B. & D. L. Hagae - Com. ap. Beauregard 1747. in 8vo. p. 9 Vogt Libror. rarior. p. 40. describes this Commandin edition surpassing that of Jean-Baptiste Memmius which was printed in Venice in 1537. It quotes Fabricius’ statement in the Bibliotheca Graeca about Memmius or Memus not having understood the subject at hand translated from a basically wanting manuscript with manifold thereby rendering his version weak. It also mentions that this didn’t mean Commandin’s was fault-free remaring the Greek manuscript he had drawn on was filled with failts. <br>Concerning Apollonius’s work Koudela states†Interest in ancient Greek knowledge increased gradually in the fifteenth and sixteenth centuries especially in Italy the leading country of Europe's culture and science of the time. Latin translations of Greek works on conic sections and other curves - Apollonius and Pappus in particular - appeared in several editions. Although some original works were also published in the sixteenth century no significant progress in the study of conic sections had been made until the work of Kepler. His contribution influenced the further development of projective geometry and can be regarded as the transition from ancient to modern geometry. The spread of Greek knowledge in the Renaissance The invention of conic sections is attributed to Menaechmus 4th cent. BC a member of Plato's Academy at Athens. Various species of conic sections were obtained by truncating an acute-angled right-angled and obtuse-angled cone by a plane perpendicular to the generator of the cone. Conic sections were also investigated by Aristaeus the Elder 4th cent. BC and by Euclid c. 325 - c. 265 BC. Their works on this subject are now lost. The works of Archimedes 287 - 212 BC contain some important results concerning the properties of conic sections especially parabolas. The greatest ancient writer on conic sections was Apollonius of Perga c. 262 - c. 190 BC. His famous work Conics consisted of eight books and contained 487 propositions. Apollonius introduced the terms ellipse parabola and hyperbola and showed that various sections of the cone can be obtained by varying the inclination of the intersecting plane. Among other ancient authors dealing with conic sections we should mention Pappus of Alexandria c. 290 - c. 350 AD the last of great Greek geometers. His main work known as Collection is valuable - among other things - because it provides an account and comments on the results obtained by his predecessors. Pappus introduced the notion of the focus and the directrix of a hyperbola Kline 1990 p. 128 .<br> <br>Apollonius’ work influenced the greatest scholars of the modern era such as Descartes and Newton. The Latin translation of the first four books of Apollonius by Gianbattista Memo appeared in Venice in 1537. The present edition of Apollonius’ Conics of the sixteenth century is based on the translation and important new edits by Federico Commandino 1506-1575 who published “classical Greek mathematical texts under the auspices of the Duke of Urbino.†Horblit: “The most influential early edition of this highly important text entirely superceding Memmo’s version of 1537â€. <br>Other sources state that in total the Conics consist of 387 not 487 propositions published in seven books with the eighth book remaining unconfirmed. <br> <br>References: Adams A-1310; Brunet I 347; David Clement Bibliothèque curieuse historique et critique: A-Aqvino 1750 p.415/6; Dibner 101; Honeyman 118; Horblit 4; Koudela L.: Curves in the History of Mathematics: The Late Renaissance 2005; Norman 57; Riccardi I/1 361 51; Commandino; Sotheran I 124.<br>Work II: Conicorum lib. V VI VII with Archimedis Assumptorum liber.<br> Pergaeus Apollonius c. 262-c. 190 B.C. author; Archimedes c. 287-c. 212 B.C author; Abu'l Fath of Isphahan or Bundari al-Fath ibn Ali c. 1190 - c. 1245 author; Borelli Giovanni Alfonso c. 1608-1679 editor; Abraham Ecchellensis 1605-1664 translator: <br>APOLLONII PERGAEI// CONICORVM LIB. V.VI.VII. // PARAPHRASTE // ABALPHATO ASPHAHANENSI // Nunc primum editi. // ADDITVS IN CALCE. // ARCHIMEDIS ASSVMPTORVM LIBER // EX CODICIBVS ARABICIS M.SS. // SERENISIMI // MAGNI DVCIS ETRVRIAE //ABRAHAMVS ECCHELLENSIS MARONITA // In Alma Vrbe Linguar. Orient. Professor Latinos reddidit. // IO: ALFONSVS BORELLVS // In Pisana Academia Matheseos Professor curam in Geometricis versioni // contulit & notas vberiores in vniversum opus adiecit. // AD SERENISSIMVM // COSMVM III. // ETRVRIAE PRINCIPEM. // FLORENTIAE // Ex Typographia Iosephi Cocchini ad insigne Stellae MDCLXI. // SVPERIORVM PERMISSV. <br> <br>Two parts in one.Text in Latin.<br>First edition. / Editio princeps <br>Florentiae / Florence: ex Typographia Iosephi Cocchini publisher; c. 1661. Folio 294x199mm.<br> <br>Illustrated with a red and black ink title decorative head- tail pieces and woodcut initials of varying sizes at openings a large number of mathematical in-text woodcut illustrations mainly diagrams throughout again of varying sizes; wide margined paper.<br> <br>Pagination: 36 415 bl. Collation: Ll: bl. half title red and black ink title 3-6 1-4 with index A1-Z4 Aa1-Zz4 Aaa1-Fff4 with errata bl. <br> <br>Very beautiful and rare work edited by Alfonso Borelli is the first edition of books<br>V VI and VII of the Conicorum of Apollonius. Concerning Apollonius Koudela states†Interest in ancient Greek knowledge increased gradually in the fifteenth and sixteenth centuries especially in Italy the leading country of Europe's culture and science of the time. Latin translations of Greek works on conic sections and other curves - Apollonius and Pappus in particular - appeared in several editions. Although some original works were also published in the sixteenth century no significant progress in the study of conic sections had been made until the work of Kepler. His contribution influenced the further development of projective geometry and can be regarded as the transition from ancient to modern geometry. The spread of Greek knowledge in the Renaissance The invention of conic sections is attributed to Menaechmus 4th cent. BC a member of Plato's Academy at Athens. Various species of conic sections were obtained by truncating an acute-angled right-angled and obtuse-angled cone by a plane perpendicular to the generator of the cone. Conic sections were also investigated by Aristaeus the Elder 4th cent. BC and by Euclid c. 325 - c. 265 BC. Their works on this subject are now lost. The works of Archimedes 287 - 212 BC contain some important results concerning the properties of conic sections especially parabolas. The greatest ancient writer on conic sections was Apollonius of Perga c. 262 - c. 190 BC. His famous work Conics consisted of eight books and contained 487 propositions. Apollonius introduced the terms ellipse parabola and hyperbola and showed that various sections of the cone can be obtained by varying the inclination of the intersecting plane. Among other ancient authors dealing with conic sections we should mention Pappus of Alexandria c. 290 - c. 350 AD the last of great Greek geometers. His main work known as Collection is valuable - among other things - because it provides an account and comments on the results obtained by his predecessors. Pappus introduced the notion of the focus and the directrix of a hyperbola Kline 1990 p. 128.<br> <br>While Koudela mentions 487 propositions in total for eight books comprising the Conics other sources mention 387 published in seven books only with an eighth book announced but its publication unconfirmed/ elusive. Apollonius’ work influenced the work of great scholars such as Descartes and Newton. A Latin translation of Conicorum’s first four books appeared in Venice in 1537 and it was not until 1661 for the present work - Conicorum’s books V to VII - to be published; the present work constitutes the most innovative or original part of the work of Apollonius. Translated from the Arabic manuscript of Abu'l Fath of Isphahan c. 1190 - c. 1245 purchased by the Medici’s during the first half of the 17th century the text of had survived only in the Arabic language. Norman states: “This was a valuable addition to the mathematical knowledge of the time for whereas Books I-IV of the Conics dealt with information already known to Apollonius’s predecessors Books V-VII were largely original. Book V discusses normals to conics and contains Apollonius’s proof for the construction of the evolute curve; Book VI treats congruent and similar conics and segments of conics; Book VII is concerned with propositions about inequalities between various functions of conjugate diametersâ€. Cajori states: “The fifth book reveals better than any other the giant intellect of its author. Difficult questions of maxima and minima of which few examples are found in earlier works are here treated most exhaustively. The subject investigated is to find the longest and shortest lines that can be drawn from a given point to a conic. Here are also found the germs of the subject of evolutes and centres of osculation.†<br>Cajori A history of mathematics 40; Brunet I: 347; D.B.I. XII 546; De Vitry 29; DSB I 191re: Apollonius & II 308 re Borelli ; III 364. Honeyman 119; Koudela L.: Curves in the History of Mathematics: The Late Renaissance 2005; Norman 58; Riccardi I /1 158 Borelli.<br><br> Size: Folio 294x199mm. Illustration: Text in Latin.<br>Illustrated with numerous decorative historiated woodcut initials of varying sizes at openings; hundreds of in-text illustrations mainly diagrams of varying sizes. Volume: Two parts in one. Pages: Pagination: Bl. 4 114 2 36 bl. Collation: Ll:1-6 1 -4 with index A1-Z4 a1-f2; 2 a1-i4. Category: Book Europe Italy; Book Science & Technology; Alexandri or Alexander or Alessandro Benatii or Benatius or Benacci, publisher unknown