Elements of GeometryAmerican Book Company, 1896 - 540 sider |
Inni boken
Resultat 1-5 av 86
Side 23
... prove that there cannot be two straight lines between X and X ' . The parallel axiom ( viz .: that through a point ... proved that we can never get rid of the parallel axiom without assuming the space in which we live to be very ...
... prove that there cannot be two straight lines between X and X ' . The parallel axiom ( viz .: that through a point ... proved that we can never get rid of the parallel axiom without assuming the space in which we live to be very ...
Side 25
... proved correct after reaching § 104. ] PROPOSITION X. THEOREM 43. If two straight lines are cut by a third straight line , making the alternate - interior angles equal , the lines are par- allel . GIVEN TO PROVE C ba A- B a = a ' . AB ...
... proved correct after reaching § 104. ] PROPOSITION X. THEOREM 43. If two straight lines are cut by a third straight line , making the alternate - interior angles equal , the lines are par- allel . GIVEN TO PROVE C ba A- B a = a ' . AB ...
Side 32
... PROVE ABC , any triangle , with a , b , and c its angles . a + b + c = 2 right angles . Draw KH parallel to BC , and from O , any point of this line , draw OE and OD parallel respectively to the sides AB and AC . * This was first proved ...
... PROVE ABC , any triangle , with a , b , and c its angles . a + b + c = 2 right angles . Draw KH parallel to BC , and from O , any point of this line , draw OE and OD parallel respectively to the sides AB and AC . * This was first proved ...
Side 36
... PROVE the angle B equals the angle C. Suppose AD to be a line bisecting the angle A. On AD as an axis revolve the ... proved in the preceding demonstration . 73. COR . II . The line joining the middle 36 PLANE GEOMETRY.
... PROVE the angle B equals the angle C. Suppose AD to be a line bisecting the angle A. On AD as an axis revolve the ... proved in the preceding demonstration . 73. COR . II . The line joining the middle 36 PLANE GEOMETRY.
Side 37
... prove it coincides with the given line . 74. COR . III . Every equilateral triangle is also equian- gular , and each angle is one - third of two right angles . Question . In how many different ways is an equilateral triangle isosceles ...
... prove it coincides with the given line . 74. COR . III . Every equilateral triangle is also equian- gular , and each angle is one - third of two right angles . Question . In how many different ways is an equilateral triangle isosceles ...
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Vanlige uttrykk og setninger
ABCD adjacent angles allel altitude angles are equal apothem axis bisecting bisector centre chord circumference circumscribed coincide construct Def.-The Defs Defs.-A diagonals diameter diedral angles distance divided draw equally distant equilateral triangle equivalent Exercise.-The face angles figure Find the area frustum geometry given circle given line given point given straight line GIVEN TO PROVE given triangle Hence hypotenuse lateral area lateral edges lateral faces locus meet middle points number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane geometry plane MN polyedral angle polyedron prism prismatic surface pyramid Q. E. D. PROPOSITION quadrilateral radical axis radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon spherical triangle square straight line joining surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Populære avsnitt
Side 30 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...
Side 466 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Side 315 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.
Side 205 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Side 36 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Side 379 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Side 138 - ... twice the product of one of these sides and the projection of the other side upon it.
Side 57 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Side 137 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Side 147 - The product of two sides of a triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side.