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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 227r, page id 00068200:0455
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Quadratum applicatae Trianguli
est aequole quod rectangulo
sub appliata parabolae, et
ideo. et summa quadracorum
prisma scilicet pypamifiti
solicet, ix quadratis rectan
Methodus fangs. nnvi
segura cujus evolatione descutitur parabolas
Xa = V
deque ejus ordinatarum summ
X= ∞y a Tunc eram adhuc
novus.
Altitudox. applicat.. y.
In parabola Xa = y 2. y. fa 2 Y. A93a)
Et summ  area 2X
in parabola subica Xa = y area = 3X
vx  y y KC 2;y. RC3, y
2A
In parabolocide XA = y a. 2X = 27a.
sunt ergo cubs quadrata applicatarum, ut
24 cubi a vertiae abscissarum. X. nc. Ya
multiplicetia
Ergo si duplicetur a vertice abscissa simpliciler
v.g.
BX. erit ejus cubus 8X3. qui est ad
cubum X. simplics, ut 8. ergo 88 y a. multipli
cubus applus cas
cetur per _. Ergo R98 ya. erit appertata
et applicata erit: RC; Na. R4 e
Hinc elegans consideratio
in para bola verticibus sceli altitudinibus multipli
catis, seu crescentibus arithmetiae s crescunt
applicata, ut Radices quadratae numerorum natu
ralium, n y. 1Rq2, y. IR43 y. let.
In Triangulo, ut radices quadratae numerorum quada
torum. y. R9 4, y. R9 9, y. etc
in cum eode parabolocid dicra, ut Radues quadratae
numerorum subicorum, Ay. A98,y. R927, y. t
Unde apparet applicatas trianguli esse medias.
proportionales inter applicatas parabolocidis, Heu–
ratianae et Parabolae, Uende sequitur trian-
gulum esse mediam proportionalem, inter Evolventem
parabolicam et Parabolam seu parabolocidem Acura
tianam, et parabolam si si Parabolocis
Triangulum et parabola sint ejusdem altitudinis
aequalis summae rectangulone, et basis. Ergo si Parabola sit 2 et Triangulum
magulo impositis conflata, est
seu solido cuidam eu cunei forma, H erit Paraboloeis  4Y
quod hinc para boloeide illuic
Parabola clauditur
 3
quare si Rectangulum circum scriplum eret ad
parabolocidem Heuratianam ut 8 ad 3. Enor
Triangulum Rctangulum ex evolvente sub rectis aequalibus evoluta et
per covolutionem descriptae aequatur figurae evolutionis.
figurae evolutionis dabitur recta aequalis curva per erolutionem
R42y _ R4 3Y.
A44
curvae
quare cum detur Recta aequalis figurae evolutae et quad ratura
descriptae
A
RgC. B Ra. Pac27 RCya
Hinc applicutae paraboloet
Nihl es
y R9C P RCY
egc 27 A
y Ex b4 RCY R9CH29 AC y3
Y AgC 8 RCYa
Rgc2us Raya
ni est ad aicum resti din  disela cireantupti et A ad 7
Parabuloeis ad Paetam eodem modo erit
R92 = R99 4. = Aqc
Aq 2  Rg 2 = 2 R92 =R98. Rg2 - 1128
2 = H. R92. A98 = cub R92.
R42 = A9c8.
b
6+
6
2C
541. Ag. 143.
ac
aecie de
paraboloeidis Heuratianae
est paraboloides
L2F