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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 92, page id 898203430:0120
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VINCENLI VIVTANE DE LOCIS SOLIVL
IC
AV
L
N Parabola. Limes Ordinationis ramorum ad or
in vertice, est ad Locum concauum FIyperbolae aequi
laterae per eundem verticem sibi circumscriptae, cuius la
rera aequantur Modulo ex anculo semirecto; nempe
recto lateri data Parabola.
TT ParabOla A B, cuius axis B C, vertex B, rectum latus BB, ac
D regulatTIX E DG, Sitque BFT Modulus a semirecto angulo extribits
Duco, l per verticem B, cum aze eransuero HB, rectoque latere BD de-
Scribatur circa axem B C FIyperbola BF. (quae erit aequilacera, quum
BD, BHI sinc aequalia) hanc esse Parabola circum scripiam, atque esse
Limitem propolucum.
1
Compleatur Roura Modulum exhibens BFT per rectam ABC cum axe
DC lemirectum angulum constitmentem, _ regulaerici occurrencem in G
ec. Sectioni rero in A, iunsaturque HIDL. regulairix Hly perbolae BF, _ IIC5.
Jam. Duum infra communem Scetionum
Bolae regulacrix DL. Temper c
magis recedat a regulatrice.
Parabolae DF ipla HIy Perbo.
19. Primi la darx Parabolae enit 2 cir
cumleripta.
Et quum ob angulos semi
rectos ad AS B, in trianoulo
ABC, SIE A C aequalis C B.
erit quoque BII aequalis IIC3
Lue recto lateri B Ld, Ced
cotinsenrem BD, Hyper-
D er primi quadratum AC equale est B rectangulo CBD, ergO A C aequalis et
LOME.
vnicuique iplarum C B, BD, HIB. Jam igitur quadraium B A, quam
rectangulum II C B duplum cst quadrati BC, led tuic aequate cst, ob
Eyperbolam requilaieram. Quadratum C. F, ergo quadrata BA, C F sun
aqualia; ideoque ramus B A ad Parabolam semiordinatxe C F in Hyper.
bola aequalis est.
Sic alius quicunque ramus BM. d per M ordinetur MO Hyperbolam
Sccans in N: ax em in O.
13. huius. Eric ergo quadraum B A ad quadra um BM vec rectangulum HCB
ad FOB, vel ob Trperbolam, ve quadratum C F ad quadratum O N,
e permucanido latus B A ad C F vF sacus B M ad ON, sed B A aequale
demonstratum est ipA C F, ergo, _ BM ipsi ON aequalis eric, de sic de
sinsulis ramis, aique semiordinatis ec. Ouare concauum huius Hyperbe.
Boix est Limes proposicae Ordinationis. Ouod crat _c.
Alicer
nOHX DI
WINaC. 1
AFCII.