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 87
... semicircle . But if the angles ABD , BAD , are not equal to one another : B B D E A D C At the point 4 , in the straight line BA , make ( I. 23. ) the angle BAE equal to the angle ABD , and produce BD , if necessary , to E , and join EC ...
... semicircle . But if the angles ABD , BAD , are not equal to one another : B B D E A D C At the point 4 , in the straight line BA , make ( I. 23. ) the angle BAE equal to the angle ABD , and produce BD , if necessary , to E , and join EC ...
Página 88
... semicircle : but if the angle ABD be less than BAD , the centre E falls within the segment ABC , which is therefore greater than a semicircle . Wherefore a segment of a circle being given , the circle is described of which it is a ...
... semicircle : but if the angle ABD be less than BAD , the centre E falls within the segment ABC , which is therefore greater than a semicircle . Wherefore a segment of a circle being given , the circle is described of which it is a ...
Página 91
... semicircle , because DC passes through the centre ( III . 1. Cor . ) Wherefore 5. The circumference AD is equal to ... semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and ...
... semicircle , because DC passes through the centre ( III . 1. Cor . ) Wherefore 5. The circumference AD is equal to ... semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and ...
Página 92
... semicircle is a right angle . And because the two angles ABC , BAC , of the triangle ABC , are together less ( I. 17 ... semi- circle , is less than a right angle . And because ABCD is a quadrilateral figure in a circle , any two of its ...
... semicircle is a right angle . And because the two angles ABC , BAC , of the triangle ABC , are together less ( I. 17 ... semi- circle , is less than a right angle . And because ABCD is a quadrilateral figure in a circle , any two of its ...
Página 93
... semicircle is a right angle , and consequently ( I. 32. ) 3. The other two angles BAD , ABD , are equal to a right angle : but ABF is likewise a right angle ; therefore ( Ax . 1. ) 4. The angle ABF is equal to the angles BAD , ABD ...
... semicircle is a right angle , and consequently ( I. 32. ) 3. The other two angles BAD , ABD , are equal to a right angle : but ABF is likewise a right angle ; therefore ( Ax . 1. ) 4. The angle ABF is equal to the angles BAD , ABD ...
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Términos y frases comunes
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