Elements of Geometry and Conic Sections |
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Page 17
... base BC will coincide with the base EF ( Axiom 11 ) , and will be equal to it . Hence , also , the whole triangle ABC will coin- cide with the whole triangle DEF , and will be equal to it ; B and the remaining angles of the one , will ...
... base BC will coincide with the base EF ( Axiom 11 ) , and will be equal to it . Hence , also , the whole triangle ABC will coin- cide with the whole triangle DEF , and will be equal to it ; B and the remaining angles of the one , will ...
Page 19
... base of an isosceles triangle are equal to one another . Let ABC be an isosceles triangle , of which the side AB is equal to AC ; then will the angle B be equal to the angle C. For , conceive the angle BAC to be bisected by the straight ...
... base of an isosceles triangle are equal to one another . Let ABC be an isosceles triangle , of which the side AB is equal to AC ; then will the angle B be equal to the angle C. For , conceive the angle BAC to be bisected by the straight ...
Page 20
... base at right angles ; and , conversely , the line bisecting the base of an isosceles triangle at right angles bisects also the vertical angle . Cor . 2. Every equilateral triangle is also equiangular . Scholium . Any side of a triangle ...
... base at right angles ; and , conversely , the line bisecting the base of an isosceles triangle at right angles bisects also the vertical angle . Cor . 2. Every equilateral triangle is also equiangular . Scholium . Any side of a triangle ...
Page 21
... base of that which has the greater angle , will be greater than the base of the other . Let ABC , DEF be two trian- gles , having two sides of the one equal to two sides of the other , viz .: AB equal to DE , and AC to DF , but the ...
... base of that which has the greater angle , will be greater than the base of the other . Let ABC , DEF be two trian- gles , having two sides of the one equal to two sides of the other , viz .: AB equal to DE , and AC to DF , but the ...
Page 22
... base EF ; then will the angle BAC be greater than the angle EDF . B D E C F For if it is not greater , it must be either equal to it , or less . But the angle BAC is not equal to the angle EDF , because then the base BC would be equal ...
... base EF ; then will the angle BAC be greater than the angle EDF . B D E C F For if it is not greater , it must be either equal to it , or less . But the angle BAC is not equal to the angle EDF , because then the base BC would be equal ...
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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.