The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 páginas |
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Página 10
... sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ... BC ' is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their ...
... sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ... BC ' is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their ...
Página 11
... side of the base . Therefore the angles at the base , & c . Q.E.D. COROLLARY ... B C For if AB be not equal to AC , one of them is greater than the other ... BC common to both , 1. The two sides DB , BC , are equal to the two AC , CB ...
... side of the base . Therefore the angles at the base , & c . Q.E.D. COROLLARY ... B C For if AB be not equal to AC , one of them is greater than the other ... BC common to both , 1. The two sides DB , BC , are equal to the two AC , CB ...
Página 13
... BC equal to the base EF . The angle BAC is equal to the angle EDF ... side of it , there can be two triangles that have their sides which are ... BC coincide with the base EF , the sides BA , AC , cannot but coincide with the sides ED ...
... BC equal to the base EF . The angle BAC is equal to the angle EDF ... side of it , there can be two triangles that have their sides which are ... BC coincide with the base EF , the sides BA , AC , cannot but coincide with the sides ED ...
Página 18
... side of it , ( I. 13. ) 1. The angles ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD ... BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD ...
... side of it , ( I. 13. ) 1. The angles ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD ... BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD ...
Página 19
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAČ ... side BC be bisected , it may be demonstrated that the angle BCG that is ( I. 15. ) 6. The angle ACD is greater than ...
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAČ ... side BC be bisected , it may be demonstrated that the angle BCG that is ( I. 15. ) 6. The angle ACD is greater than ...
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AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle