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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 81, page id 898203430:0273
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=273
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VARTAR: DISPOSITIONVM LMMT. LIBER HI.
ir pci ai 
nia
D aucem necessario seguitur ex demonstratione sui COnverS, dum pro-
BOnatuI ve lequitur.
N Parabola. Ouadratum rami cuiuscunque ex axis ver-
tice ducti cum quadrato semirecti lateris, aequatur
quadrato ex summa ejusdem semirecti; cum seemento
axis ab ordinata per rami terminum abscisso.
EIT Parabola A B, cuius avis B C, vertex B, ac lemirectum laciis
D BD, quod ips B C in directm PONAtE, d SIE GNICLNqUe PAmUS
BA, ex A vero ad axem ordinetu AC. Dico quadrata simuI AB, BD
requari quadrato agoresuti C D:
Ouadratum enim AB aequatur quadra-
iiS AC, CB, sed AC aequatur 2 duplo
rectansuli CBD (quum sIE BD semire
Atum) erod quadratum B A aequale eR
duobus rectangulis C BD cum quadrato
CB, _ addico verinque communi qua-
denco FD erune duo simul quadrata AB,
BD aequalia duplo Fectanguli C BD cum
quadratis CB, BD; Sed haec omnia con-
ficiune vnicum quadratum CD: quare duo AB, L
aqualia. Ouod crat _c.
Manifectum igitur est hinc, Locum proposiratu subcentarum esse
ad concauum expositae ParabolX. Ouod dc. SssisA
lit
e
P R O POS
12
onic
imi
Ocus mediarum Arithmeticarum inter partes aata
1. linea, (5 ad ipsam ordinatarum, est LOCuS pla-
nus, nempe recta datae aequidistans per interuallum
ipsius dimidio aequale.
IT AB data vecunque secta in C, ligue Et CIdCM SB ParasCLa de B
ea distans per inceruallum dimidium iptius A B. DicO rectam F. I.
esse