Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 páginas |
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Página 11
... rectangle is that which has all its angles right angles , but all its sides are not necessarily equal . A rhombus is that which has all its sides equal , but its angles are not right angles . A parallelogram is that which has its op ...
... rectangle is that which has all its angles right angles , but all its sides are not necessarily equal . A rhombus is that which has all its sides equal , but its angles are not right angles . A parallelogram is that which has its op ...
Página 59
... rectangle ABCD will contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rectangle AEFD as 7 to 4 , or as AB to AE . The same rea- soning is applicable to any other ratio than that of ...
... rectangle ABCD will contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rectangle AEFD as 7 to 4 , or as AB to AE . The same rea- soning is applicable to any other ratio than that of ...
Página 60
... rectangles , & c . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of their bases by their altitudes . Let ABCD , AEGF be two rectangles ; the ratio of the rec- tangle ABCD to the rectangle AEGF , is the ...
... rectangles , & c . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of their bases by their altitudes . Let ABCD , AEGF be two rectangles ; the ratio of the rec- tangle ABCD to the rectangle AEGF , is the ...
Página 61
... 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 parallelogram ...
... 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 parallelogram ...
Página 63
... rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square on AB is equivalent to the squares on AC CB , together with twice the rectangle contained by AC , CB ; that is , AB3 , or ( AC + ...
... rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square on AB is equivalent to the squares on AC CB , together with twice the rectangle contained by AC , CB ; that is , AB3 , or ( AC + ...
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.