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Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl
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ABCD abſurd added alſo altitude applied arch baſe becauſe Book called centre circle commenſurable common cone conſequently contained Coroll cube deſcribed diameter divided draw drawn equall fall fame fide figure firſt follows fore four fourth greater half Hence join leaſt length likewiſe magnitudes manner mean meaſure mediall Moreover names odde P R O parallel pentagone perpendicular plane prime priſmes produced PROP proportion proportionall pyramide quall ratio rationall rectangle remaining reſiduall right angles right line ſaid ſame ſay Schol ſecond ſegment ſhall ſide ſolid ſome ſpace ſphere ſquare Take taken thence theſe things third thoſe touch triangle whence wherefore whereof whole
Σελίδα 25 - ABC, with its adjacent exterior ABD, is equal b to two right angles ; therefore all the interior, together with all the exterior angles of the figure, are equal to twice as many right angles as there are fides of the figure ; that is, by the foregoing corollary, they are equal to all the interior angles of the figure, together with four right angles ; therefore all the exterior angles are equal to four right angles, PROP. XXXIII.
Σελίδα 99 - Proportions that are one and the fame to any "Third, are alfo the fame to one another.
Σελίδα 289 - Right-lined plane Angles equal , from whofe Points equal Right Lines be elevated on the Planes of the Angles, containing equal Angles with the Lines firft given, each to each ; Perpendiculars drawn from the extreme Points of thofe elevated Lines to the Planes of the Angles firft given, are equal to one another.
Σελίδα 96 - AE is the fame ai . c." hiultiple of the whole CF + FD, as the one AE is of the one CF, that is, as AB is of CD ; therefore GE (£)~ b £4 AB; and (<r) fo AE, which is common, being takeri c ^ away, there remains GA=EB, Therefore, &c.
Σελίδα 268 - j from whence it begun to be moved. XXII. The Axis of a Cylinder is that fixed Right Line about which the Parallelogram is turned. XXIII. And the Bafes of a Cylinder are the Circlet that he defcribed by the Motion of the two oppofite Sides of the Parallelogram.
Σελίδα 140 - XA number oddly odd, is that which an odd number meafureth by an odd number.
Σελίδα 33 - Pjthagoiat his theoreme, becaufe he was the inventor of it. By the help of •which the addition and fubftraftion of fquares are performed; to which purpofe lerve the two tdllowjng probleuies.