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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 141, page id 898203430:0169
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=169
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.86
# 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.

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Bola C L. K ad suum lemirectum, ex contructione, ergo quadratum F. L.
ad LII eA ve ipse semitransuerlus EL ad luum lemirectum; nempe L II
est media geometrica inter praedicta lemilatera Hyperbola C L K, hoc
est porest quarcam sux sigurae partem, sed L. EI iplam coninsit ad L, Cr-
BO iuneta LEIR est 2 Alymptoros delcriprae CFL K. Similiter LP el al- 2 10. lceun
tera eiuldem Almpcocos: erie ereo quadeatum LHI, Ciuc quadratum libi di C onsc.
aequalis reCEX BF C ex Moduli inventione) aequale rectangulo RO P, quin
bus communi addito, vel dempro reccangulo OF O, eric recEanGULUM
RF P aequale quadrato BO, sed recrangulUm R I. P aequale cs quadrato
F B C quum tocum quadratum RB aequale sic quadrato L F, SIVC duobus
EB, BF, quibus commune est quadracum BF) ergo ee quadraum BO
ip(i F B aequale erit, ideoque ramus minimus F. B ad datam Hyperbolam
ABC aequalis semiordinatae BO, vsque ad deseripeam GL K.
Sic praecerea quilibet alius ramus L. A, de per A ordinata D C deleri-
pram lecans in Cx, axem vero in D.
HTabebie ergo quadracum rami F B ad quadratum F A rationem rectan. b 28. huius
guli b ND L ad rectanSUIU NBL, vel ob Ayperbolam C L R vE c C 21. prime
quacratum D C. ad quadraum B O, sed permurando quadratum F. B COniC.
Equatur quadrato B O, ve nuper demonstrauimus, ergo de quadratum
E A quadrato DC, Euc ramus L. A ad datam Hyperbolam ABC semi-
Ordinatae DC in deleripia  L. K aequalis est. Quod etat etc.
Lur hinC laCEFA F R, F. PrianGulI CIrCUMA(YMpTOTALIS RE P eNle
t Quoniam veraque iplarunt cansentium BF, L. II pores quartam par-
tem sux figurae, acque iplae BF, L. FI inter se sune aequales, constat tâm
dulae Flyperbola, quam invemi Limicis lemiaves conuenios aequales este.
L Lps ine Lis yperbolici.
TOrandum est insuper Lemitrae s  Ls usoa Polle res
proporcionalium FS. Sitiac ve suntua Lemilaterum data ad lemirectum.
semirecto dale LI) petbola, ABC, erir BF media proporrionalis, inter lemi
latera F B, BT; quare ve lemilacus cranluersum P B 2d Semirectum DY.
ia erit quadratum L.B ad B l, de componendo; ve duo sinul lemilatera
E. B, BI ac secc 23 La n Gua ala 2. BL, HL CH
ita quala L.F. Vel la Guaealus le  de Guaal B L AC e
ad quadracum HIL, sive ita quadratum BF. ad F. L, vel ad rectangulum
BE. 5. Iinc ica lemiaxis BF ad F. S; quare F. S est quarca proporcionalium
Post
Lu cangulum sub semiaxe cransuerso P. B datae Hyperbolae in quartam
ita Temuas cxanuet uS da dlaII.
Sumpra enim F. S certia proporcionali post EB, FL, ac BT aequali