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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 70, page id 898203430:0262
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=262
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.90
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VI TELC L LOCIS SOLL
F AI M A HII.
 R2OC. XLI.
N crianculo aegururi; cuius anculus basi oppositus sit
acutus, perpendicularis; quae ab altero basis termino
super oppositum latus ducitur, potest duplum rectanculi
sub partibus lateris eiusdem à perpendiculari abscissis,
ona cum quadrato partis basim attinsens.
SFOrriangulum aquicrure, d aeurangulum ABC, ex A vero, l
L mino balis AC, ducta sic in lacus B C perpendicu.
lariS A D, quae cadec inera iplum criansulum C quo
niam anguli B, C, ponuneur acuti.) Dico quadratum AD
aequale esse duobus rectanoulis BD C cum quadraio DC.
Nam, per praecedens Lemima, est quadratum AC aequale
duobus rectanoulis BCD, SCd AXC RGUANEE duobuS BDC
cum duobus quadratis DC, ergo a quadratum A C, hOc
est duo simul AD, DC, aequantur duobus rectangulis BDC
cum duobus quadraris DC3 dempto isitur communi qua
draro DC, remanet quadratum AD aequale duobus rectan
sulios BDC cum quadralo D C. Quod erac demonstrandum
P R OP, O S HiF. I. Om. X
YT igitur pOnum ocendamus, ponatur eriangulum ABC rectan
V Sulum ad B, cuius camen lacus AB in prima fgura minus sic relio
quo BC, e conra vero in secunca suc maius, de cum bali AC ad pun
ctum C consticuatur angulus AC D ips B A C aequalis. Fx quonigni au-
sulus BAC est acutus, duo simul B AC, ACD crune duobus rectis mi
nOrCS, dC PrOPterea CD conveniet cu AB, ve in puncto D, quod in
prima cadet exira productam AB, quum angulus B A C, sivc A C D
maior sic angulo AC B, e in secunda cadet in iplam AB, quoriam gu.
gulus BAC, CIC ACD minor eA, angulO AC B.
Praeterea, facto C. polo subrentarum, ex eo ducatur in prima AGurZ quae-
cunque subrenla C I sCCanS aXEM D P inter D, et B, de alia quaelibet C
M secanS inter B, _ A, atque insuper alia C F secans infra A. In secun-
da vero agatur guaeuis CL lecans axem inter D, de A, ee alia guxlibet
CP intra A.
Amplius, Lablenta OMes C L. CB. C. M, C C ETanSTCTANEUT CX PUN.
a0 A ranquum poto ranluertalium vigue ael recteo 1E. BO, MH. AC,