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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0083
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P
2. For au Parallelorrams, mulciply etil P’expen-
upon; and che Product is thie Area. Becaule alI
Becaule char Line will be equat lohe heishl
Such Ligures are equal ro Rllates et le Tae eta LdI.
or equal Bale and Alcicude.
3. For al Plane Friancles, muloiply hale che
Perpendicular ler tall trom any Ansie, by the
oprolice le, or halfchac lde by che Perpendicu
lar, and che Produet is che lue ea; because
Trianoles are chehalves ol Paralleux rams ot che
lame or equal Bales and Alcirudes.
For a Prapezium, Where wo illes are Pa
rallel, mulciply che dumm ol che Lalalles lde
(b and a) by halt (p) che Leeat.
dicular lec fall trom any side, by che side ic Falls ot each Triansle in che Polyson, and cheir Bales
wilt be allo equal, because chey are sides ot 2
Thus in a HexaCON, WI
and ehe Distance som the
ot any otche sices 10 Xards
The Summ Ol C siueS
Side is 8 Yards.
onter r0 che Midale
6X8 = 48. votose
halt is 24. Which mulciplied by 10 produces 240
5. For any other Traxezium or any Multane ula
Plane Figure, resolve it Diagonally into Lrian
oles; and add the Areas oF thole Triangles
(Found by che 3d Problem) into onc summ
ivtich will be che erue Area of che whole. Lhu
suppose a Trapezium whole Sides are nol paralle
divide it into uvo Triangles by a Viapota
and lec fall a perpendicular trom che othor Ansie.
therero; then multiply che whole Base b
BalE che Summ, (or BalF che Bale by l
aote  ot che Perpendieutat,  Lbuur
Pards, che area ot che exacon
7. For all Circles, mulrixly hals rhe Circumte-
rence by che Radius; because every Cirele is e.
Quat 10 d heclanele L, one ot vitole Lcgo o ce
Periphery, and rhe ocher ihe Radius. AS Archi
medes Hac detonacca. For Practice, meature
the Semi-diamerer, then (ay, 25 100O, ZTAY 3 2
(0 is the Semi diamerer ro che Circumference:
ewhich found, mulciply by halt che Diamerer (OF
Radius) che Produet is che Area.
8. For a Sector of a Circle, mulriply che Radius.
or one oF its Leos By HaIF hC ArCH, (Or BaIE chC
IS ThC,  ea.
Base 24, ie5 haIF
Summ ot che Perpend. 12, its t3lE 5, 5.
90
hacius by chc whole Areh ihe Produet Biveo EC
Content.
che Sector Mnhuine onche arke and allo che Area ot
che Trianele, and Cubtctact enal et  uns
9. for au Segments of Circles,  cu sred bi
Erom hac ot he Sector, al LLCI Id EK Is CIC Lat
OE hC Serment.
1D. For an Ellipsis, mulciply che longe Ba
merer by the Morrell, and exrract the square
Root oF the Product, ic sires che Diamerer ot
Circle whole Area is equal eo the Area oF the FI
C s
lipsis; because che Diamerer of such a Circle i
mean Proporrional olneen ine aclesot
AI. For a Parabola, mulriply the eneire Ordi-
a L Laa, 2 daxtim coloured
Circle abour che Nixpte
nare by the Abscissa or intercepted AX; chem
double chac Prodult, and divide che holeby 
S. For all Repular Fieures or Polysons, mulci
ly che hale summ ot aIl the Sides, by che
lenech oF a Line dravn From che Centet W chc
midate ot any one Side, che L SIres EHC
Area
the Ouollene 1InC Area