Chauvenet's Treatise on Elementary GeometryJ. B. Lippincott Company, 1887 - 322 páginas |
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Página 17
... these three is a right angle , and the other two are together equal to the right angle BOC ; hence the sum of the angles AOD and BOD is equal to two right angles . 14. COROLLARY I. The sum of all angles having a b 2 * BOOK I. 17.
... these three is a right angle , and the other two are together equal to the right angle BOC ; hence the sum of the angles AOD and BOD is equal to two right angles . 14. COROLLARY I. The sum of all angles having a b 2 * BOOK I. 17.
Página 20
... hence they are equal ( 16 ) . In like manner it can be proved that the opposite angles AOD and BOC are equal . EXERCISES . 1. Theorem . — The line which bisects one of two vertical angles bisects the other . 2. Theorem . The straight ...
... hence they are equal ( 16 ) . In like manner it can be proved that the opposite angles AOD and BOC are equal . EXERCISES . 1. Theorem . — The line which bisects one of two vertical angles bisects the other . 2. Theorem . The straight ...
Página 22
... Hence the triangles coincide throughout , and are equal . PROPOSITION VIII . - THEOREM . 23. In an isosceles triangle the angles opposite the equal sides are equal . Let AB and AC be the equal sides of the isosceles triangle ABC ; then ...
... Hence the triangles coincide throughout , and are equal . PROPOSITION VIII . - THEOREM . 23. In an isosceles triangle the angles opposite the equal sides are equal . Let AB and AC be the equal sides of the isosceles triangle ABC ; then ...
Página 23
... Hence the tri- angles are equal , by Proposition VI . EXERCISE . Theorem . - A line drawn from the vertex of an isosceles tri- angle to the middle point of the base is perpendicular to the base , and bisects the vertical angle ...
... Hence the tri- angles are equal , by Proposition VI . EXERCISE . Theorem . - A line drawn from the vertex of an isosceles tri- angle to the middle point of the base is perpendicular to the base , and bisects the vertical angle ...
Página 33
... Hence PD = P'D , and PE P'E . P E D A -B P PDP ' is less than PEP ' , by Proposition XX .; therefore PE , the half of PEP ' , is greater than PD , the half of PDP ' . 2d . If the lines lie on opposite sides of BOOK I. 33.
... Hence PD = P'D , and PE P'E . P E D A -B P PDP ' is less than PEP ' , by Proposition XX .; therefore PE , the half of PEP ' , is greater than PD , the half of PDP ' . 2d . If the lines lie on opposite sides of BOOK I. 33.
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Chauvenet's Treatise on Elementary Geometry William Chauvenet,William Elwood Byerly Vista completa - 1887 |
Términos y frases comunes
ABCD adjacent angles altitude angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise Find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane angle plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Pasajes populares
Página 200 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Página 133 - The area of a rectangle is equal to the product of its base and altitude.
Página 137 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Página 117 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Página 214 - The acute angle which a straight line makes with its own projection upon a plane is the least angle which it makes with any line of that plane.
Página 113 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Página 38 - The sum of the three angles of any triangle is equal to two right angles.
Página 184 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Página 128 - Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k.
Página 52 - 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.