The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 páginas |
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Página 15
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to ...
Página 16
... equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut ... angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the equal sides ...
... equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut ... angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the equal sides ...
Página 19
... equal to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC ... angles . Let BAC be the given rectilineal angle , it is required to bisect it . A Take any point D in AB , and from AC cut ( ...
... equal to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC ... angles . Let BAC be the given rectilineal angle , it is required to bisect it . A Take any point D in AB , and from AC cut ( ...
Página 20
... equal parts in the point D. Which was to be done . C A D B PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in ...
... equal parts in the point D. Which was to be done . C A D B PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in ...
Página 21
... angles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal ( 15. Def . 1. ) to the base CG ; therefore the angle CHF is ... angle CBA be equal to ABD BOOK I. 21 THE ELEMENTS OF EUCLID .
... angles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal ( 15. Def . 1. ) to the base CG ; therefore the angle CHF is ... angle CBA be equal to ABD BOOK I. 21 THE ELEMENTS OF EUCLID .
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 81 - The angles in the same segment of a circle are equal to one another.
Página 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 22 - ANY two angles of a triangle are together less than two right angles.
Página 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Página 24 - Any two sides of a triangle are together greater than the third side.