Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 3
... proposition and the Book in which it has been announced or de- monstrated . The expression ( 15. 1. ) denotes the fifteenth proposition , first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post ...
... proposition and the Book in which it has been announced or de- monstrated . The expression ( 15. 1. ) denotes the fifteenth proposition , first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post ...
Página 8
... its parts . 11. All right angles are equal to one another . 12. " Two straight lines which intersect one another , cannot be both " rallel to the same straight line . " pa- PROPOSITION I. THEOREM . If two triangles have two sides 8 ...
... its parts . 11. All right angles are equal to one another . 12. " Two straight lines which intersect one another , cannot be both " rallel to the same straight line . " pa- PROPOSITION I. THEOREM . If two triangles have two sides 8 ...
Página 9
... PROPOSITION I. THEOREM . If two triangles have two sides and the included angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or equal in all respects . Let ABC , DEF be two ...
... PROPOSITION I. THEOREM . If two triangles have two sides and the included angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or equal in all respects . Let ABC , DEF be two ...
Página 19
... proposition , the ob- lique line AC cannot be equal to the oblique line AH , which lies A nearer to the perpendicular AB ; B therefore it is impossible that H C E D F BC can differ from EF : hence , then , the triangles ABC and DEF are ...
... proposition , the ob- lique line AC cannot be equal to the oblique line AH , which lies A nearer to the perpendicular AB ; B therefore it is impossible that H C E D F BC can differ from EF : hence , then , the triangles ABC and DEF are ...
Página 22
... proposition to the case where the side AB lies in the same direction with DF , and AC in the same direction with DE , is necessary ; because the angle CAI would have its sides parallel to those of the angle EDF , but would not be equal ...
... proposition to the case where the side AB lies in the same direction with DF , and AC in the same direction with DE , is necessary ; because the angle CAI would have its sides parallel to those of the angle EDF , but would not be equal ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore