Full text: From Aristarchus to Diophantus (Volume 2)

XIV. CONTINUED. 
B. Apollonius of Pekga .... pages 126-196 
The text of the Conics ...... 126-128 
Apollonius’s own account of the Conics . . . 128-183 
Extent of claim to originality .... 132-133 
Great generality of treatment .... 133 
Analysis of the Conics 133-175 
Book I 133-148 
Conics obtained in the most general way from 
oblique cone 134-138 
New names, ‘ parabola ‘ ellipse ‘ hyperbola’ . 138-139 
Fundamental properties equivalent to Cartesian 
equations ........ 139-141 
Transition to new diameter and tangent at its 
extremity 141-147 
First appearance of principal axes . . . 147-148 
Book II 148-150 
Book III 150-157 
Book IV 157-158 
Book V 158-167 
Normals as maxima and minima .... 159-163 
Number of normals from a point .... 163-164 
Propositions leading immediately to determination 
of evolute of conic 164-166 
Construction of normals ..... 166-167 
Book VI 167-168 
Book VII . . 168-174 
Other works by Apollonius . • . . . . 175-194 
(а) On the Cutting off of a Ratio (Xóyou (nroroprj), 
two Books 175-179 
(/3) On the Cutting-off of an Area (ycoptou àiroTopi]), 
two Books ....... 179-180 
(y) On Determinate Section {òuopiapévr] Topi)), two 
Books 180-181 
(б) On Contacts or Tangencies (eVa^at), two Books . 181-185 
(e) Plane Loci, two Books ..... 185-189 
(£) Neiffeis (Vergings or Inclinations), two Books . 189-192 
(rj) Comparison of dodecahedron with icosahedron , 192 
(0) General Treatise 192-193 
(t) On the Cochlias ....... 193 
(k) On Unordered Irrationals . . . . . 193 
(X) On the Burning-mirror . . . . . 194 
(/r) 'SÌKVTÓKIOV ........ 194 
Astronomy 195-196 
XV. THE SUCCESSORS OF THE GREAT GEOMETERS . 197-234 
Nicomedes 199 
Diodes .......... 200—203 
Perseus ■ 203-206 
Isoperimetric figures. Zenodorus 206—213 
Hypsicles 213—218 
Dionysodorus .218-219 
Posidonius ......... 219—222
	        
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