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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 36, page id 898203430:0228
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36
VINCENTIL VIVLANL DF LOCIS SOLIDIS
ceangulum CDB dimidium es quadrati DE, adeoque duo C D B aequan.
cur quadrato D F, sed duo C DB aequaneur differencix inter rectaneu
Ium A D B, _ guadratum DB (per Lemma praecedens) ergo de qua-
deacum D F ip(i differentix aequale cAt: & hoc de qualibet simili ordinaca
_c. Ouare concauum huiusmodi FIliplis est LocuS propolica Ordinarionis.
Ouod exat dC.
P R OPOSTTTO LM.
Ocus Ordinatarum potentium differentiam inter re
ctanculum sub coadditis, (5 quadratum addita, est
ad concauum Parabola vereens ad additam, 55 cujus
vertex sit occursus data cum addita, rectum vero la
tus eidem datae sit aequale.
IT data A B, de quiacunque addica B C, ee per verricem B Circa.
axem BC cum recto latere datae A R aequale describatur ParabO2
BD. Dico hanc esse Locum propolitum: hoc est ordinacam C D posse dit
ferentiam inter rectangulum coadditarum
ACB, de quadratum additae BC.
Nam difterentia inter rectansulum
ACB, _ quadratum B C es RCCEANGU
Jum ABC, quod, ob Parabolam, aequale
est quadrato ordinata C D (quum Pon2.
TUT AB rccrum latuS) ergO C D poreAt
praedictam disserentiam: ee hoc de qualibet simili ordinata dec. Ouare
concauum huIUS PaTabOl CA Locus proPOua Ordinationis. Quod erad
PROPOSITIO ET.
Ocus Ordinatarum potentium differentiam inter re
etanculum sub coadditis; (5 quadratum super addia
ta est ad concauum Parabola vercens ad superaddi-
tam, cuius vertex sit occursus datae cum eadem super
addita; rectum vero latus ipsi datae sit aequale.
Et data AB. a Tuperaddica quaelibet AL. ae per vercicem H. Cla
axem AC, cum recto ipsi AB aequale delcribatur Parabola AD. Di.
Co hanc esse Locum PropOTum: hoc est ordinatam C D posse disseren-
ciam incer recrangulum AC. B sub coaddiris, et quadrarum superaddia
a.
Difteren-