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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 39, page id 898203430:0231
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=231
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
# Lines: 46 recognised, mean confidence 0.89
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

ovmara ot L. La. 
1+O
L
ROPOS
Ocus Ordinatarum potentium differentiam inter qua
dratum datae, es rectanoulum partium, est ad con-
vexum Fyperbolae aequilarerae, cuns centrum sit punu
ctum bisecans datam, semiaxrs vero transuersus possit
triplum quadrati ex datae dimidio.
GTE data AB seca bilariam in C, per quod sic C D perpendicularis,
quae possic criplum quadrati AC, vel CB, dE CUI CCHETO C, PeF Ver-
ticem D (uc deleripta Fy perbola requilatera F DF. Dico hanc eAe Locum
propolitum. Nimirum ordinatam quamlibet C FY posie disserentiam inter
quadratum AB, _ recrangulum AC B.
SuMatur C Y ipS C D aequalis, _ in directum, ac per Y Aat FErperbola
LIM OpPOlIa ip(I FD F, ee super AB tiant quadrata AF, AM, quo
rum laceribus F F, L M OCCUErAHE prOduCX CD, CH in H, O, P. .
Eyperbolis vero in LI, R.
Ex quoniam quadratum NC quadru.
plum est quadrati AC (eo quod (IE CN
dupla AC) ee quadratum CD criplum
est ejuldem AC, ex constructione, ergo
reliquum rectangulum ODN, vel IND
aquale est quadrato A C, vel quadrato
NE, sed idem IND aequale est quadra
ro lemiordinatae ex N in Hyperbola
aequilatera F. DF, ereo quadratum NF
quadraco ciuldem lemiordinatae Cx N x-
quale est, nempe Hyperbola eran(it PCF
E angulum quadrati. lidemque demon-
Arabitur huiulmodi oppolicas Sectiones
erantire per reliquos angulos F, L, M:
sed rectangulum IND ad R PFI, vel O
Ed N ad OTTP CAE vE rectanGUlUI E NF
2d F PF, vel ve rectangulum AC B, Cive
quadratum AC ad rectansulum AC B,
atque est permurando rectangulum ODN octensum aequale quadrato AC.
ergo ee rectangulum OHIP rectangulo AC, B aequale est: sed quadratum
G HI es difterentia inter quadratum C P, de rectangulum OTI P, de CA.
quadratum AB aequale quadrato (3P, e rectangulum AC B equale re-
etansulo OHIP, ergo idem quadratum GFI erit quoque difterentia intee
quadratum datae AB, _ rectangulum sub partibus A C B; veluti etiam
quadratum C. D est difterentia inter quadraun C N, vel AB, de re
ctaneu.
2 Cx 22. lib
l.c