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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 131, page id 898203430:0159
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OADINALLONNM CONIC. CIMITTBVS LIB. L
Secet itaque descripta Hyperbola verticalem tansenrem BG in O, Ct.
que alius quieunque ramus DS, de per S ordinata YV.
Et quoniam ex terminis Famorum DS, DA, DB, ad axem datae TIy-
perbolae ductae lunc ordinatae SV, AD, BB, _ NL elt ModuuS _C.
quadrata FamOruM DS, D A, D B erun inter se ve ~ rectangula NV L,
18. huius.
NDL, NBL, vel ob ErpeiBOlaM T AL C ve D quadraca semiordina D 21. primi
CaTUM VY, DA, BO. Sed quadracum rami D A aequacur, imo idem. Conic.
es ac quadratum semiordinatae D A sibi homologx, ergo de reliqua reli-
quis, singula singulis, e latera laceribus, neupe ramus DS Pemiordina-
Ex VY, _ ramuS DB semiordinata BO aequalis exic, de lic de omnibus.
Ouare concauum huiulmodi descripiae Hyperbolae est Limes. propolica
Ordinationis. Ouod erat etc.
ctum daxe Hyperbolae, ita esse OL al L L componendo
Scensum fuie ve OD ad DR, nempe ve transuersum ad re-
ivitur erit MOA dd AO. Vel r summa laterum ad rectum. ita OD du
D P, quare D P inceruallum a cenro Limitis vlque ad originem elt
quarta proporcionalium si Aac ve summa lacerum ad reccun datae TTyper-
bolee, ita distancia inter cenerum ejuldem Hyperbolae, e originem ad
aliam.
2. Et quoniam PB est difterentia inter D P, DB, erit P B, dictantia
incer centrun Cimitis de verricem datae FIrperbolae, aequalis differenciae in-
ter praedictam quartam inventam PD, ec ramum minimum DB.
3. Lc quum rectangulum D P E demonstratum requale si quadrao
PE. Cemiaxis cransuerus P L. invenei Limitis poterit rectangulum sub
seomenis axis PD, nempe a centro Limiris vlque ad originem, siuc ad
balum crianguli circumseripei, in PF. ab eodem cenro rique ad eiuldem
trianguli verricem.
Voniam vero NI. ad L. X est ve transuertum Ad X HI)PEIDOL ad
ctum, quandoque esse Hyperbolam requilareram, quandoque vero inx-
summam lacerum ejusdem, constat ex hac constructione inventum
Limitem AL C, Cu.uS NL est transuersum lacUS, de L X rC-
qualium laterum in ratione, aue maioris, auc minoris ina qualicais, PrOUI
emlis  pold cela lacio laliietti dalce dec lutum iplo iucerlit.
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