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 106
... plane and another part without it . Demonstration . By the definition of a ... planes cut each other , their common intersection is a straight line ... MN , it will be perpendicular to every other straight line PQ drawn 106 ...
... plane and another part without it . Demonstration . By the definition of a ... planes cut each other , their common intersection is a straight line ... MN , it will be perpendicular to every other straight line PQ drawn 106 ...
Page 107
... plane , and thus it will be perpendicular to the plane MN . Demonstration . Through a point Q , taken at pleasure in PQ , draw the straight line BC in the angle BPC making BQ = QC ( 242 ) ; join AB , AQ , AC . The base BC being bisected ...
... plane , and thus it will be perpendicular to the plane MN . Demonstration . Through a point Q , taken at pleasure in PQ , draw the straight line BC in the angle BPC making BQ = QC ( 242 ) ; join AB , AQ , AC . The base BC being bisected ...
Page 108
... plane MN . It is manifest that this incli- nation is the same for all the oblique lines AB , AC , AD , & c . , which depart equally from the perpendicular ; for all the trian- gles ABP , ACP , ADP , & c . , are equal . THEOREM . and 332 ...
... plane MN . It is manifest that this incli- nation is the same for all the oblique lines AB , AC , AD , & c . , which depart equally from the perpendicular ; for all the trian- gles ABP , ACP , ADP , & c . , are equal . THEOREM . and 332 ...
Page 109
... plane . The least distance of these lines is the straight line PD , which is at the same time perpendicular to the ... MN , Fig . 186 . every line DE parallel to AP will be perpendicular to the same plane . Demonstration . Let there be a ...
... plane . The least distance of these lines is the straight line PD , which is at the same time perpendicular to the ... MN , Fig . 186 . every line DE parallel to AP will be perpendicular to the same plane . Demonstration . Let there be a ...
Page 110
... plane MN , it will be parallel to this plane . Demonstration . If the line AB , which is in the plane ABCD , should meet the plane MN , this can take place only in some point of the line CD , the common intersection of the two planes ...
... plane MN , it will be parallel to this plane . Demonstration . If the line AB , which is in the plane ABCD , should meet the plane MN , this can take place only in some point of the line CD , the common intersection of the two planes ...
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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.