# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0595
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0595?run=74
# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0595
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=595
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000595.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 97 lines, status machine
# Lines: 97 recognised, mean confidence 0.85
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

rom) and is in Nords thus: s Rectan-
sle under theSides of ihe Cone  Wothe Square
of the Diameter of the Base :. S0 is the Di-
stance betreen the Verrices  Ihe Cone ana
of the Section, to ihe Lacus lcctum.
TII. Pravis J. Flence it rou have the Verte
describe ic on a Plane.
in that cake as mans. Abscissae a5 ou please
then find berwmeen chem ely and che L. a
tus Rectum, (0 many Hean Proporrional
Wohich it rou rigliely apply co che Aris il
and Parameter oF any Parabola, ris eaHC LC
For dran a Riehe Line For theAris, anet
N O F A F LO N.
Tet the Side A B fOF the ConC) be a Che
Side BC == b, the Diameter of the Base AC
= c: L et S B be called o a and E I == e b
Wheretore the Frianeles B C A and F IV
beins Similar, B C (Or b) will BCFO A C (OF
C):: 25 F L (= e b) iS FO NV L a FOUTTH PrO.
portional; Wohich in chis Nocarion will be 2)
Or CC. THeretore N I = ec.
AIo because che Friansles A BC and BF P
are similar, FP, or irs Equal IO wil (rhis
Wvar) betound t0 bc05.
DEMONSZ RAFFON.
K F is a Mean Proportional berween N L and
EO, (the Seomenes oF che Diameter co which
it i5 perpendicular) Wvheretore chC D OF TK
NVTO, Wrhich in chis Nocation is eoc0.
Diride Theretore e00c bY the Abscissa E I == c b,
ihe Ouorient is =, = Wwtich must be ehie L. atus
Rectum: Forirmulciplied into che Abscissa maties
eocc the Square oF che Ordinate LH. And
From this Fqualier Berrveen the Square and the
Rectanste, Apolonius save chis Section che Dame
OE che Parabola.
cOROLLAKIC.
J. Ftence may che Laus Rectum De Tound
very casilY, iF 1D b, C, and 0c, (thac is,
to the Side of the Cone parallet to the Axis of
the Section, toche Diameter of the Base; and
2o che Latus Primarium,) You tind a Foureh
Proporcional; Cor chat will De LE chePa-
rameter, DE Latus Rectum == P L.
I. And il sou mutripir che Parameter
both abore and belor che Line by a (the
Side ot the Cone in wrtrich is etie Verrez
Ot the Section) vou will hare chis Ouan-
ridy
40cC
. Wrhick may easily be resolred
into these Proportionals;
ab. cC:: a0.
0c0
occ
Wrhich sires Apollonius his Canon eo sind
he Lacus Rectum, (L.ib. Y. PFOP. 1I. Bar.
be semi-ordinates; and laslY, chicix Fnds O
Lexcreams ucaus sertus a sete rhe Curre
OE che Parabola
NV. Praris 2. Flarine e rertea. aliet A
ca17,
dinace, L0 find che Farametor, Scomerei
Apply righely che Semi-orallate R L
and cake From the Verrex O, L L == LR
Ttien chrough F draw a Parallet (a5 LL L
to che Ordinate PK, and produce OR 10
LL; (0 wil FIC DC che l’arameter Ol Larm
Rectum Toughe.
For itie Frianeles OK L and OHF
Octne similar, FI. LIE :: FF (= LL). CL
And conscsuens L LL ls a cumaneter.
V. And Mce che Parameter in chis was. OL
Nocation is =, let il in ehe last Fieure
callece Locus bt che Parabola: L. N wis bC
0c
OceCC
iotict diri–
be applied eo che Parabola in ihie Posirion
C MI. Then vilt N be che Poine erhich is
b 6 Squara
0c0
dect D) Ie Paramerer B Bires De E02
the Abscissa L. I. S Sers that ihe FOCHS
is alvays distant from u Vertex os the Paxa
b0la by  os ihe Lcrametet.
VI. PraxI 3. FLaVHIB Cus Bained MMC FOCUS
he Curre ot a P’arabora may be described
ver more eatlr and readili: IF rou drai
turtc che AxIs OF (L18. last) and rhen an
Ordinace in any Poine, 25F. Atrer chis rake
che Abscissa O F in jour Compalses, anc
Cettins one Fooc in che Focns HV, crols etie
Ordinare in C, (0 Mail che Poine C bc in
che Parabola. And chius may as mans
Poines 25 rou wilh De spcedily found.