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Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl
No preview available - 2017
ABCD abſurd added alſo arch baſe becauſe Book called centre circle commenſurable common cone conſequently contained Coroll cube deſcribed diameter divided draw drawn equall fall fame fhall fide figure firſt follows fore four fourth given greater Hence join leaſt length likewiſe magnitudes manner mean meaſure mediall Moreover multiplying 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 thereof theſe things third thoſe touch triangle whence wherefore whole
Page 2 - XV. A Circle is a plain figure contained under one line, which is called a circumference ; unto which all lines, drawn from one point within the figure, and falling upon the circumference thereof, are equal the one to the other. XVI. And that point is called the center of the circle. XVII. A Diameter of a circle is a right-line drawn thro' the center thereof, and ending at the circumference on either fide, dividing the circle into two equal parts.
Page 27 - 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.
Page 76 - Right-lined figure is faid to be infcribed iri a. right-lined figure, when every one of the angles of the infcribed figure touch every one of the fides of the figure wherein it is infcribed.
Page 101 - Proportions that are one and the fame to any "Third, are alfo the fame to one another.
Page 291 - 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.
Page 98 - 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.
Page 270 - 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.
Page 142 - XA number oddly odd, is that which an odd number meafureth by an odd number.
Page 35 - 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.