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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 17
# Folio 4r, page id 00067979:0007
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Constructio Problematis solidi dati,
ope sectionis Conicae datae,  (irculi inventi
Esto problema solidum datum:
lonatur (p
g1 Or- 113
-r +
a
e rm - 1
We 6 + 2g
+lV trm V +rnV +rx 510.
et F extrn.
Recta b, et A sumentur pra bitrio
4 e Y - 2b  n = + 1. Sectionis Conicae latus
latus rectum Y transversum  quod transversum in parabola est infinitum.
pZ Sectionis conica date latus rectum sit , transversum T. Descripta ergo intelligatur
1 B +4 ibus RF + rg cb 1 79
vel ((I_ F +B, + +1+ 2Y(0. Siponimus 19, f0. et H0. (mujus fara faciemus, ut ita sit ubius posito
eique applicetur recta
M  f2OrE, 1+ + 2tdq (quod in Parabola e 0, ut calculus dabit)
DCGFAE
porro
At54 ex data V4, ita habetur: sectioni cunicae datae, accribatur Triangulum
Sectio conica data descripta intelligatur
DCGFAE, ut vides figura 1. et
quae est circuli, fig. 2. quae est Ellipseos, figura 3 quae est Hyperbolae, et fig. 4 quae
sive portiones
est parabolae, ita scilicet duae sectiones oppositae, DCG, FAE unam sive figuram,
sive sectionem in constituere intelligantur duos habentes vertices oppositos, er
A. C. per v axem sive latus transversum primarium AC. junctos unam
sive figuram sive sectionem constituere intelligantur, quod in Ellipsi et Circulo non
habet opus admonitione, nam in illis duae portiones opposite conveniunt; in Hyperbola autem
ubi divergunt, admonendum utique fuit, in Parabola vero multo magis, ubi una sectione
descripta EAF, alteram sive des haberi describi impossibile est, qui cum sit alterius
ut ita dicam mundi, sive infinite distet abtionc, nam Parabola potest intelligi
Hyperbolae genus, sed cujus latus transversum AC sit longitudinis infinitae, Quod ergo
in ea describendo fieri non potest, calculo supplebitur ut mox patebit
ectioni ita descripta applicetur recta ENF e V4 ab axc ad angulos rectos bisecta
in N, et utrinque ad curvam terminata: denique ex puncto E vel F educatur normalis
5D, vel FG, quae scilicet sectioni oppositae occurrat in D. vel G. ea erit + dq quaesita
in Parabola autem ubi ED, quippe infinita duci non potest, calculus docet esse 89++D
ea proinde ductu illo esse opus.
+ 2r2 M - d g (+ 4b) 24b
a L
(1 - ab +74
= 6b+ 247
e
et 25 0
 +
61 82Gr +B. -
Explicatis ergo literis ad constructionem ita veniemus: in recta ED sumatur ab E versus D. recta
EP , MY erigaturque  perpendiculari
PK 1 P, +b. An eadem recta, producta
si opus est sumatur velsus  recta K6 et ex puncto 6 a plaga ( versus
plagam s sumnt parallela axi AC, recta
velut centro, radio
f12
54 1 2 denique puncto 2
+VGr 9+D PGt deminuta destribatue radius siralus
qui secabit sectionem Conicam datam in punctis  ex quibus in rectam indefinitam,
agi pavullelam per punctum s transcntem denisse perpendientares YV, eunt 1 quaesitae
P
Hextra
rectangulum
DEE