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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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Rishe Sine in the Generarine Circle, (as BD, Space APL C  Mus d ceual eo chree seni.
bd) tocether with the Arch of that Sine, AD
eriple oFrhe Generarins Circle.
Ocherwile chus
8. F.
The Rectanele AE is equal eo rmo Cirgles, al
the Semi-Ellipsis AC C e eo onc, Wheretore che
remainHS Space AeC F C must also be equal r
cireles, and cheretore che whole Cycloidat SpaCe
Manner ot  Generacten et ine lctora abore de-
Semi-circle, and consequens, e semi cycloidat
Space equal ro chree demcireles. L. L. D.
lirered: For since che Rishe Linc C F is equal co sition l had nom MP. Fumphry Diccon, Who is
D F must be equal eo che Ouadrancal ACK AD;
For che sereral Arks of che morins Circle do eve-
ey where generare Righr Lines equal eo chem
selres; Wheretore any Semi-ordinace drawn co
Morr and plain, and depends on che Arictimerick
OE Infinires. Thus
che Curre ofthe Crcloid must be compounded oF do, do, dO; ecc. are suppoled eo be in Arichme.
f Or D F, viz. 2 Righe Line equal ro rhe Parr rical Proporrions, and consequenty (o will che
oftthe Ark chac hach revolved, and oE b d and Lines 00, 00, CO, ecc. Which trom the Nature
BD che Righe Sine ot chac Ark in che Generatins (oF che Cycloid are all equal severally e0 rhole ArKS:
Circle. R: F. D.
Corollaries.
cloid a Riehe Line may most calily be tound equal
2o any given ArK oF a Circle, op 1o ies whole Cir-
cumterence; and consequently the Guadrarure ot
che Circle may Geomerrically be had it chis Cyeloid
be a true Ceometrical Curre, 25 indecd ir is HOE.
evhere dranon equal co che Righe Lines bd, BD
and bd; che Curve Line connectins cheir Exrre.
miries will be an Elliphs (by a ProPOL. which vo
vill find under che mora Elliprical Space) for the
vohole Aporesare ot all Thele Righe Lines, or the
Ellipeica lSpace wils be double ot che Semicircular
One; 1. c. 25 Be is rO B B; and consequenty the
cions, will bc 10 as matis eqsual 10 che Brentett
23F ED 2 (BV ProP. 2. OF DF. WV allis 5 Arith. Infi-
Curvilincal Space Ae C D A Wis bc equal ro che nic.) Wheretore the space la S= =SV, bu
Semicircular Space ADC. A.
2. DF (1. C. = DC L CF) Ouadrant D A, Where
Fore since thae Whole BC= to a Semi-circle, che
Remainder BD F FO must al(0 bC equal e0 a912-
Cycloidal Space C DS must be equat t0 chcec
Semi circles. 8. F. D.
AFanE; buE BD =DC (by Cor. 2.) Wheretore cF che Curre Wc an lcars B0a) ou dcleti.
vil be equal EO FO: and che lame way ot argu
supposing it eo descend with the prearest pOstBL
ing will alvays prove ef abore equal eo fe bc- Switrnets, IS IBC R 6) a Ca. LHIS f0Bi Bet
tou; Wheresore all etie Indiritibles in each beins noulli, L Thinte, Arst proxosed, 25 a problem 10 be
equal, the Space ee A f F will be equal ro che discovered, and ir hath otren been solved; but
SpaCC FG L. HenCO,
Cirele, (becaule one side is che Radius and the
ortier the Semi-circumference) chac is, is equal 10
the Semi-elliplis CDA; Wtctct H MC OF
Philos. Transact. N. 268. In the Acta Fruditorum
Inrectisarion Cor chis L’ine by Zames Bernoulli.
CrONOS, the sman, a Constellacion in che
Norchern Femisphere consictins Ot 35 Stars.
CPLINDEK; che Hollon wichin every Piece
EE VOU FaKC The Ouadran e  LMIII DC CC S, OF Ordinance is called her Concave Cylinder.
Wrhac remats, Wtieh is the Trapezium C CGL C,
must be equal co the ocher Ouadrane of the FI-
ExEINDER, is a Solid Body, made by che
lipsis, or eo ille semicirele. Bur ic was proved in Rorarion ot a Rectanoled Paralle lopram about one
10 ec AfF; Wheretore che lrilinear Ligure
F F F C A must 2ls0 be equal 10 the Semi-
I. Since overy Cylinder hach a C ircle toc IIs
ercte; are consequenls che inhoie semiepesoidal Bale, il vill be vecy proret 10 denoreis Bise
ctiuo
Fhis is proved trom che Consideration OF the
P. Isence eis plain, thac by means et ee C).
2. It VousapPosc de, D e, ance ul 1odctes
anorter Puch CHele, ana sES TOer HaIF EO Q SCMII
circle as vell a5 iis upper one; bur in the love
halt che Figure FG F. = to che Fieure ee Af F in
the upper half; Wheretore couner-chanee chem
and che SpACC C E A F A must also bC equal e 2
The folloue Demonstration ot che lame Propo-
very stiltul in chines ot chis nature. Tis very
The Fixure is a SeMezeloid, where che ArKS
Now rhele being a Selres et Arichmerical PrOPOE.
ES D= 10 che Whole Circle; Wheretore the whole
The Linea Celerimi Descensus, 25 Eis called, or
very briesy and eahly by Mr. Zoln Crat 
4.Z1s pran, that che Cycloidat Space is alvays Lips. FOr May 1690, p. 217 there is a Method ot
Triple of the Generatins Circle.
Fot IHC Rectanole BC F C is equal coche whole
CVEMA, che same wvich Embroin.
Cor. 3. TIaC CH LLHICat PACC LC L. lras equat set irs Sides.