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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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atgle GR (BV 5a2 Lvel.) and as triil presene-
Iy appcar, il vou rey ic Alsebraically atrex ete man-
ner oF che Demonstrations in chac B0Ok. Wherc-
lore chese cvo Remainders must be 10 eacti orter.
25cheir Wholes: : (1. c.) a5 che Square oF C F 10
the Square OF F O:: Or aS C F Square: F O
Square. And ihen ic will Aaria cus;
CFB: FOO: CF O: Rectanete DC H
Or Inversely: AS;
EOD: CFD:: Rectangle OGR: CFD.
Thac is, ehe Square oF F. O, and che Rectangle
OCR, hare etie Paie Proporrion to the Pame
chins, and consequeney are equal one 10 ano-
THCF.
And ehis will Be che Case everr wwhere, let che
RGymptores run never. (0Far. And sinee the FuT-
thec vou eo trom the Verrex ot che Anple C, che
lonxer must che Lines CR, Pr, OF necessitr groir,
Forthe Square oE s F (che Ordinate) i5 = 10
the Rectanple D F R (By che Hyperbola:) WVhere.
fore che Rectarsle D F P (= Square F 5) I51O
che Square FC, a5 Lacus Transversum, Is eO L arus
Rectum oF ehic Hyperbola C F HLG; 1. c. i5 the
Square DE: Square A B. Wherctore che ROOES
Ot chele squares ill be also proporrional; and
consequency Fs: FO:: D F: AB. The FOr.
mer vo Terins oF wrhich, beins cach an Indirilible
tince. ehe Rectanele berween CR and )C, is il.
OE cherivo Hyperbolick Spaces, ir will Folloi, chav he
vays he Tame, viz. = O P Squatc, eic Morrer wtiale Spaces are in che lame Proporrion.
must CC. Fg, concinually erow; and conse-
queney decreale infinicels, a5 che others increase
intinicelr; (i. C.) The Curve will infinitely approach
+o the Asimptote.
Buc vec eher can nerer Coincide, or meet wicti
one anocher: l’or it che Points C and , or 5 and
J. Xc. Mould erex come ro be Coincidene; it will
be as the Rectangle D F P: F G. Square : : 50
vill C F Square bC 10 FG. Sgnare (For C F Square
and F O Square, wonld ehien be ete same ihins.
Thac is, Rectangle D F F. Wvould bC = 10 C F
Square, which is urtertr impossible; as is plain
FrOMI 6d 2. Fucl.
Wheretore B CBB: G E HO:: DF: A B
Oc C FHlG: 8C V C:. AB: DF
Hencer H rou sindche Quadrature ol an Hyper-
bola, ertole Parameter, and Latus Transversum
are equal; rou may square any orter Hyper
bola.
In Pbilosoph. Pransac. N. 34. There is 2 Ouadira
cure oF. chc EExperbola; by an Insinite Series ot Ra-
Tional Numibers.
In Numb. 53. There is a Mechod communicareat
Wheretore chese Lines are erue Asimprotes, a5 by Sir Christopher Wren, Cor erindine Glasses oF an
Apollonius named ehem from ehis impossibilies of LIxperbolick Figure.
Coincidence wich che Curve ot rhe Hyperbola,
wrtren placed in chis Posirion, Vid. Apoll. ProP. 1.
Lib. 2.
HIVPERBOLE sin Rhecorict) is a Figure whict
represenes chings Ercater, lesser, Verrer; (90. Than
in realier ches arc; and is used in Discourse when
our ordinary Terms are t00 wenk Or 100 ArOnS,
and carry no proportion wich our Idea; and least
ve Bould spcak 200 licile, We Ay our, and Car 100
much, Or ehe contrary: Asco expressthe Siritinele
ot a Hlorle, onc Bould Pay he was swister thonthe
Wind. TEche Ronness oF a Perlon, Thar he move
Porver than a Snail.
FIYPERBOLIOK-SPACE, is che Area OF SpaCI
contained becwmeen che Curre ot an ZTy perbola, and
che whole Ordinate.
Ans LBdbolick- SpnCC C, L. LL O, lsto any orher
Hyperbolick Figure oF che Tame heiphe s ch8,
Cutiose Latus Rectum and Transversum, 25 in ehic
ArPERDOLICOM ACOTOM, is a solid
made by cheRerolucion oF che Infinire Area oF itie
Space concained berween rhe C urre and the ACimp
corc, in che apollonian Typerbola, curnins round
thac Asymprore; this produces a Solid or Body infi-
nicels lonz; aud vec as Torricellius plainty demon-
Arares sho pare ic ehis Name) ic is equal 10 2
Finice Solid Or Bodv
HVPLRCATALEETICK Verse. See Depo-
sition.
HXPERCATHARSIS, is a PursC chac Worts
100 MuCh.
HYPERCHIAIS, is 2 Crivical Excresion above
measure.
HYPERDISTLLABLE, is a Wordt OE more
Syllables chan rvO.
HIXPFROON, arethe rvo toles in the uxper
ParE OF che OPa Polati, Wtich receive che Pirui-
tous Hlumours, trom che Mammillarr Processes.
and atcer cher are separared, discharee them ac ehe
Circle) are equal, and also borh equal 10DP, (che Mouch. Thro chose a Branch oF che fitch paix Ot
Fatus Transversum OF che Former Spacc) a5 the
coniueace Anc A B, is 10 che L aciis Transversum
Nerres passes coctic Palate, Vrula and Cums.
HTPEREPHIBROSIS, is 100 much Sveat
ine
HITEERSARCOSIS, Is an EXCrelence OI Fleta
in any pAEI.
IREERLHYRON, in Archirecture, i5 a larRC
Table usually placed over Gates Or DoOrs oF etie
Doriek. Oeder, abore che Chambrante, in Torm ol
2 FriZC.
ATPHEN, is an AccenE in Crammar, chac im
plies Luo N’ords acc 10 be joynid, a5 Male. Sanus.
u
trrmiotictu