Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New England |
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Page 43
... bases and equal altitudes , are equivalent . Demonstration . Let AB ( fig . 96 ) be the common base of the Fig . 96 , two parallelograms ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the ...
... bases and equal altitudes , are equivalent . Demonstration . Let AB ( fig . 96 ) be the common base of the Fig . 96 , two parallelograms ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the ...
Page 44
... ABCD , ABEF , which have the same base and the same altitude , are equivalent . 167. Corollary . Every parallelogram ABCD ( fig . 97 ) is equivalent to a rectangle of the same base and altitude . THEOREM . 168. Every triangle ABC ( fig ...
... ABCD , ABEF , which have the same base and the same altitude , are equivalent . 167. Corollary . Every parallelogram ABCD ( fig . 97 ) is equivalent to a rectangle of the same base and altitude . THEOREM . 168. Every triangle ABC ( fig ...
Page 46
... ABCD , AEHD , have the same altitude AD ; they are conse- quently to each other as their bases AB , AE . Likewise ... base by its altitude , provided that , by this product , we understand that of two numbers which are the num- ber of linear ...
... ABCD , AEHD , have the same altitude AD ; they are conse- quently to each other as their bases AB , AE . Likewise ... base by its altitude , provided that , by this product , we understand that of two numbers which are the num- ber of linear ...
Page 47
... ABCD . 175. Corollary . Parallelograms of the same base are to each other as their altitudes , and parallelograms of the same altitude are to each other as their bases ; for , A , B , C , being any three magnitudes whatever , we have ...
... ABCD . 175. Corollary . Parallelograms of the same base are to each other as their altitudes , and parallelograms of the same altitude are to each other as their bases ; for , A , B , C , being any three magnitudes whatever , we have ...
Page 48
... ABCD is equivalent to the parallelogram ADKL , and has for its measure EFX ... ABCD is equal to the product of the altitude EF by half the sum of the sides ... base AB , the point H will also be the middle of AD ; for the figure AHIL is ...
... ABCD is equivalent to the parallelogram ADKL , and has for its measure EFX ... ABCD is equal to the product of the altitude EF by half the sum of the sides ... base AB , the point H will also be the middle of AD ; for the figure AHIL is ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circle circular sector circumference circumscribed common cone consequently construction convex surface Corollary cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent figure formed four right angles frustum Geom given point gles greater hence homologous sides hypothenuse hypothesis inclination inscribed isosceles join less let fall line AC measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN point F polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium sector segment semicircumference side AC sides AB similar solid angle sphere spherical polygons spherical triangle straight line tangent THEOREM third side triangle ABC triangles are equal triangular prism triangular pyramids vertex vertices whence
Popular passages
Page 43 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 3 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 4 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Page 16 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 58 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 158 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
Page 32 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 142 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 136 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 154 - ABCDE, and equal in altitude to the cylinder, is said to be inscribed in the cylinder, or the cylinder to be circumscribed about the prism.