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 14
... shown , that BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a ...
... shown , that BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a ...
Página 26
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . * Let ABC be a triangle ; any ...
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . * Let ABC be a triangle ; any ...
Página 27
... shown that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . B A E Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the ...
... shown that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . B A E Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the ...
Página 30
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . Ir two triangles have two angles of one equal to two angles of the other ...
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . Ir two triangles have two angles of one equal to two angles of the other ...
Página 34
... shown that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27. 1. ) to CD . Where- fore straight lines , & c . Q. E. D. C PROP . XXXI . PROB . To ...
... shown that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27. 1. ) to CD . Where- fore straight lines , & c . Q. E. D. C PROP . XXXI . PROB . To ...
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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.