# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0856
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0856?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 806933011:0856
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=856
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000856.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 90 lines, status machine
# Lines: 90 recognised, mean confidence 0.87
# 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.

r4. The Poles oF the Sides of any Triatee
CTID, do on che Suatace oF chelrlobe, contitule
another Friangle nx m, erhich may be called Sup.
plemental ro che Triansle CHID; For che Sup
Plements oE che Angles and Sides oF che Triangle
nxm, are equal 10 che sides and Aneles ot che
Trianele C D HI.
DEMONSTRATION.
quener, che ruo Pomes ot incerlection ale al cu
distance of a Semicirele From each orher.
Frianele must be less chan a Semicircle.
9. The oppolite Angles at the intersection ol
cvo Circles are alivars equal, because the same
Planes constiture boch Angles; chacis, che Angle a
is equalto che Ansle b. Sec Figure belovr.
20. In a Spherical Triansle, it che Sum oF che
Less oF any Angle be Grearer, equal, or lels tham
a Semicircle; the internal Angle at the Base is aC.
cordingly grearer, equal, or less than the ourvard
and opposite one; and consequenur, the Sum o
ihe cvo incernal Angles at che Baseis grearer, equal
or less chancvo Rixhr Anpses.
B. AII preat Circles must cut cach orher inro
EO equal Parrs; becaule cheir common Inter-
section is a Diameter OF the Sptere; and conse
EOROLLARY.
Hlence eis plain, Thar everr Side oF a Spheric
DE MONSTR ATYON.
From che Poinrs CHD, 25 Poles, deseribe cree
preac Circles X A y,
ib  b27
RT m n, X B n Z, then id
Ouadrane = A
because m is the Pole
OF HI Cy, and x Or P che Pole OFC A, cheretore
Ouadrant = M LC, Meretore n m = lR = Sus
and 21 Lo Oua
supplem
IE OFC A == AnelC TTOD
C = B ∞, cherctore n X = B 3
E oE Ansle IIOD, and n Y =
plemene oE che Ansle D H6.
, Lhac che Friangle n F im constimred Be-
crcch chechreenexe Poles, has its chrec Sides
longer chan cb, and consequents, CC AlIlC
= a) ill be bisser than che Angle c d b. Pro-
perry 3. Bur il a c-I c d be equal ro a Semicircle.
chen dc will beequal ro c b, and che angle
Anslec d b. And in the Trianele d c b, becaule
0-)= cb is lelsthan ab; theretore a c is greate
than c d, aud consequenty che exrernal Ansle ad
is grearer chanche Anslea; chac is, chanthe An
sle b, the internal anele at the Base.
Alo, since the Angle a dc-- the Angle C d
ervo righe Angles, cheretoreche Ansle a d c-
ehe Angle a is greater than evo Righe Ansles, (o
22. In an Tolceles Sph. Friangle, il one oF che
equal Lces is greater, equal, or lels than a Qua-
dranc, che Angle is accordinsly greater, equal, or
dels than a Rishe one.
Ansle L and che Ansle Lihe dupplement et
che side CD.
13. Any Angle oF a Friangle, wich che ditter-
tence os the oter tvo, 1s sels chan rvo RiphE An
Bed. Foe, an is tels canx m + mn.
That i6,
2L = D =2L = 6- F 2L -FI.
Theretore,
C  HT -- D =2 l
12. The Sum oC che chree Sides os evers Sph. (For sinee 2 L = D = 2L = C + 2L - H:
Friansle, is lels chana Circle.
FOF C d I5 le (S chan c b: I b d, Woheretore a c-
dc d an must be less chanche Sides a c b  adb
Sec che Figure abore.
Thac is,
2L = D = + L = C - H
12 THC HCAIMIE OL AHIY SpDerCK Anere, IS AII YDY EtAIISICLHI L, C, atia LL CWIII DC2 l-
Ark OF 2 great Cirele described From the Angular I II = 4L Y D; ihen by cakins awar. 2 l
Point, and precilelr 90 Deg. distane trom ic; char
se matiue ihe Auguloe boue ve Edle ot rra,
Eucte.
trom boch Sides, and cranstering D You il have
C  HI = D =2L. Q. F. D.
16. TFruo Friangles are mutually Equiangular,
ches nec allo auenatis Eguilarecal: hoc becante
iher
and Angles equal ro the Angles and Sides ot
che Lllansle CFlD, lare chac che srearell
Side n m iS che Supplement oF the greatest
IEa C. Jc d De preater than a b, d c must be