Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 páginas |
Dentro del libro
Resultados 1-5 de 18
Página 61
... construct a rectangle having the altitude AF ; the par- allelogram ABCD is equivalent to the rec- tangle ABEF ( Prop . I. , Cor . ) . But the rectangle ABEF is measured by AB × AF ( Prop . IV . , Schol . ) ; therefore the area of the ...
... construct a rectangle having the altitude AF ; the par- allelogram ABCD is equivalent to the rec- tangle ABEF ( Prop . I. , Cor . ) . But the rectangle ABEF is measured by AB × AF ( Prop . IV . , Schol . ) ; therefore the area of the ...
Página 87
... construct the triangle . The two given angles will either be both adjacent to the given side , or one adjacent and the other opposite . In the latter case , find the third angle ( Prob . VII . ) ; and then the two adjacent angles will ...
... construct the triangle . The two given angles will either be both adjacent to the given side , or one adjacent and the other opposite . In the latter case , find the third angle ( Prob . VII . ) ; and then the two adjacent angles will ...
Página 88
... construct the triangle . E A Draw an indefinite straight line BC . At the point B make the angle ABC equal to the given angle , and make BA equal to that side which is adjacent to the given angle . Then from A as a center , with a ...
... construct the triangle . E A Draw an indefinite straight line BC . At the point B make the angle ABC equal to the given angle , and make BA equal to that side which is adjacent to the given angle . Then from A as a center , with a ...
Página 94
... construct a rectangle equivalent to a given rectangle . Let AB be the given straight G H E F line , and CDFE the ... constructed on the lines AB , AG will be equivale ! t to CDFE . For , because AB : CD :: CE : AG 04 GEOMETRY .
... construct a rectangle equivalent to a given rectangle . Let AB be the given straight G H E F line , and CDFE the ... constructed on the lines AB , AG will be equivale ! t to CDFE . For , because AB : CD :: CE : AG 04 GEOMETRY .
Página 95
... constructed upon the given line AB .. PROBLEM XXIV . To construct a triangle which shall be equivalent to a polygon . Let ABCDE be the given polygon ; it is required to construct a triangle equiva- ' ent to it . A B given Draw the ...
... constructed upon the given line AB .. PROBLEM XXIV . To construct a triangle which shall be equivalent to a polygon . Let ABCDE be the given polygon ; it is required to construct a triangle equiva- ' ent to it . A B given Draw the ...
Términos y frases comunes
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone 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 given angle greater Hence Prop hyperbola inscribed intersection join latus rectum less Let ABC lines AC major axis mean proportional measured by half meet 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 side BC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC triangle DEF vertex vertices VIII
Pasajes populares
Página 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.
Página 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Página 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.
Página 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.
Página 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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.
Página 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. 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.
Página 30 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.