Elements of Geometry and Conic Sections |
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Page 11
... vertices of two angles not adjacent to each other . Thus , AC , AD , AE are diagonals . F E 19. An equilateral polygon is one which has all its sides equal . An equiangular polygon is one which has all its an- gles equal . 20. Two ...
... vertices of two angles not adjacent to each other . Thus , AC , AD , AE are diagonals . F E 19. An equilateral polygon is one which has all its sides equal . An equiangular polygon is one which has all its an- gles equal . 20. Two ...
Page 69
... vertices B and C are in a line par- allel to the base ( Prop . II . , Cor . 2 ) . The triangles ADE , BDE , whose common vertex is E , having the same altitude , are to each other as their bases AD , DB ( Prop . VI . , B Cor . 1 ) ...
... vertices B and C are in a line par- allel to the base ( Prop . II . , Cor . 2 ) . The triangles ADE , BDE , whose common vertex is E , having the same altitude , are to each other as their bases AD , DB ( Prop . VI . , B Cor . 1 ) ...
Page 104
... vertices in G. Hence the sum of all the triangles , that is , the surface of the polygon , is equivalent to the product of the sum of the bases AB , BC , & c .; that is , the perimeter of the polygon , multiplied by half of GH , or half ...
... vertices in G. Hence the sum of all the triangles , that is , the surface of the polygon , is equivalent to the product of the sum of the bases AB , BC , & c .; that is , the perimeter of the polygon , multiplied by half of GH , or half ...
Page 127
... vertices not lying in the same face . 3. Similar polyedrons are such as have all their solid an- gles equal , each to each , and are contained by the same num- ber of similar planes . 4. A regular polyedron is one whose solid angles are ...
... vertices not lying in the same face . 3. Similar polyedrons are such as have all their solid an- gles equal , each to each , and are contained by the same num- ber of similar planes . 4. A regular polyedron is one whose solid angles are ...
Page 131
... vertices A and E draw the L planes AÏKL , EMNO perpendicular to AE , meeting the other edges of the parallelo- piped in the points I , K , L , and in M , N , O. The sections AIKL , EMNO are equal , because they are formed by planes ...
... vertices A and E draw the L planes AÏKL , EMNO perpendicular to AE , meeting the other edges of the parallelo- piped in the points I , K , L , and in M , N , O. The sections AIKL , EMNO are equal , because they are formed by planes ...
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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project No preview available - 2016 |
Common terms and phrases
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 27 - VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the...
Page 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 17 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 148 - I.), that every section of a sphere made by a plane is a circle.