# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0852
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0852?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 806933011:0852
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=852
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000852.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 69 lines, status machine
# Lines: 69 recognised, mean confidence 0.84
# 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.

Demonstration.
Onthe Cenere a wichthe Distance a c, deleribe
a Cirele, which will Incerlect boch che ocher sides
Ot che Triansle, andrhen Z d Will reprelenethe Sum
Ot the Legs da and a c: de ill reprelene cheir
Disterence, and d fWvill reprelene che Diserence 0
che Segmenrs of the Bale made by che FaII oF the
Perpendicular a P.
Then I CaY, d c: dZ:: d c: df: ThacIS, The
Dase is to the Sum of the Lezs:: as the Difference be-
omeen thetrmo Sides is tothe Disserence of the Serments
of the Base; 25 is apparene trom Prop. 67. OF Par.
dies Sixch B0ol, alter drawins che Prickt Lines
eo and f2.
And ihen the Cale will Aanel chus.
C ASF III.
GirenE, O, B, all thechree Sides. Requiredche
Ansles. Sec the Figures betore.
FCay, by chis Ariom, B: H YO:: F -O: X,
Which expresses che Disserence ot the Scomenes ot
the Base, =df in che Figure.
And chen havine sounc X; hale B. I tall X = d P,
the greater Scemene, and half B - halF X = pc
the lesser, by irhich means the ervo Righrangled
Triansles a d p, and a p c, will be solved casily:
FOr d a: Racus:: d p: Co sine oP che Angle d.
and a c: Radius: : 25 p c: 10 che C0 sine oF che
Ansle c.
Tue Operation of the Six l ases of Oblique
angled Triangles.
C ASF L.
Civen H, O, c. Requell
O: 5, c:: H: 5, 
The Numbers ot ea Lansie, ave a5 Tollons.
38 OC
   tt
=91
II = 780
=
=
e. 8920946 = 780
Sum = 12. 4770632
S, b = 9. 9031477 - 53 81
54 = 347.G
9. 5849685 = 22 37
E H
Find sirst che Anele B, by Case 1. etien vill a
be tnoivn.
5, c : :: 5, a5
5, a=
2. 5739154 == 374 9
9. 9864273 = 2OqY5
B = 2. 3133142 = 945
Siven (I, O, c. Required B.
S,C = 9. 5849683 = 22 39
Sum == 12, 5603427
P A 8F 1L
_en c, b, O. Required FI.
Ot = 22037
2. 5739154 = 374
5, b = 9. 9031084 = 53 8
Sum = 12, 4770238
HI = 2. 8920553 = 780
CASE IV.
Civen t, a O. Required b, c.
H+9: 11 0.. ,2K op. v. 2)
-
+I 1 O = 1154 9
FTalE Z OpPOsIC AnBles = 37 52