Euclide's Elements ... compendiously demonstrated, by I. Barrow. Transl1660 |
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... whence it not fel- dome comes to paffe , that through the want of Conjunctions and Adjectives , Ergo , rurfus , & c.there arifes difficulty and occafion of doubting , efpe- cially to fuch as are but little vers'd therein . And in the ...
... whence it not fel- dome comes to paffe , that through the want of Conjunctions and Adjectives , Ergo , rurfus , & c.there arifes difficulty and occafion of doubting , efpe- cially to fuch as are but little vers'd therein . And in the ...
Page 9
... whence b draw two right lines CA , A BBC dA C. dx . • Wherefore the Triangle A CB is equilateral , e23 . def . Which was to be Done .. CB . Then is AC c › T Scholium . After the fame manner upon the line AB may be defcribed an Ifofceles ...
... whence b draw two right lines CA , A BBC dA C. dx . • Wherefore the Triangle A CB is equilateral , e23 . def . Which was to be Done .. CB . Then is AC c › T Scholium . After the fame manner upon the line AB may be defcribed an Ifofceles ...
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... whence A3 and CD are parallel.which was to be Dem . PROP . XXXI . A E B From a point given A to F draw a right line A E_parallel to a right line given BC . From the point A draw a right line AD to any point of bax . C 27.8 . 23 , T. the ...
... whence A3 and CD are parallel.which was to be Dem . PROP . XXXI . A E B From a point given A to F draw a right line A E_parallel to a right line given BC . From the point A draw a right line AD to any point of bax . C 27.8 . 23 , T. the ...
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... whence it follows , 2. That if in one triangle , two angles ( taken fe- verally , or together ) be equall to two angles of another triangle ( taken feverally , or together ) then is the remaining angle of the one equall to the re ...
... whence it follows , 2. That if in one triangle , two angles ( taken fe- verally , or together ) be equall to two angles of another triangle ( taken feverally , or together ) then is the remaining angle of the one equall to the re ...
Page 28
... whence alfo AC , BD are parallel . PROP . XXXIV . A B. ACD D , and ABD BC bifects the fame . In parallelograms , as ABCD , the oppofite fides AB , CD , and AC , BD , are equall each to o- Dther ; and the oppofite angles A , are alfo ...
... whence alfo AC , BD are parallel . PROP . XXXIV . A B. ACD D , and ABD BC bifects the fame . In parallelograms , as ABCD , the oppofite fides AB , CD , and AC , BD , are equall each to o- Dther ; and the oppofite angles A , are alfo ...
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Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl Euclides No preview available - 2018 |
Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl Euclides No preview available - 2018 |
Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl Euclides No preview available - 2017 |
Common terms and phrases
ABCD Abfurd alfo alſo bafe baſe becauſe bifect binomiall centre circle commenfurable common meaſure confequently confir Coroll cube number defcribed demonftrated diameter dodecaedron draw drawn EFGH equiangular equilaterall faid fame proportion fecond fegment fhall fide fince firft foever folid fome fore fphere fquare number fuperficies fuppofed greater Hence Icofaedron incommenfurable infcribed irrationall leaft leffe leffer likewife line AC magnitudes mediall odde number oppofite parallel parallelepipedons parallelogram pentagone perpendicular prifmes prime number PROP proportionall pyramide quall rationall line rectangle refiduall line refidue right angles right line AB right line given right-lined figure Schol ſhall Space AC ſquare thefe thence thofe thoſe triangle triangle ABC w.w.to be Dem whence wherefore whole line
Popular passages
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.
Page 35 - AB, AC, containing the right angle. "join AE, and AD ; and draw AM parallel to CE...