Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 sider |
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Side 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 ...
Side 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 ...
Side 60
... rectangles , & c . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of therr 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 therr bases by their altitudes . Let ABCD , AEGF be two rectangles ; the ratio of the rec- tangle ABCD to the rectangle AEGF , is the ...
Side 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 XAF ( 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 XAF ( Prop . IV . , Schol . ) ; therefore the area of the parallelogram ...
Side 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 , E AB2 , 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 , E AB2 , or ( AC ...
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Vanlige uttrykk og setninger
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected CA² chord circle circumference cone contained convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given point given straight line greater hyperbola hypothenuse inscribed intersect join latus rectum 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 quadrant radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium segment side AC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Populære avsnitt
Side 27 - If 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 two triangles will be equal.
Side 157 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Side 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Side 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.
Side 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 10 - CHG; and they are adjacent angles; but when a straight line standing on another straight line makes the adjacent angles equal to one another, each of them is a right angle; and the straight line which stands upon the other is called a perpendicular to it; therefore from the given point C a perpendicular CH has been drawn to the given straight line AB.
Side 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.
Side 22 - 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.
Side 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.
Side 41 - It follows that either couplet of a proportion may be multiplied or divided by any quantity, and the resulting quantities will be in proportion. And since by...