Elements of Plane and Solid GeometryAmerican Book Company, 1903 - 384 σελίδες |
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Σελίδα 21
... extremities of the line . e II . Any point without the perpendicular is un- equally distant from the extremities of the line . 12 D B I. Let CD be to AB at its middle point D , and P be any point on CD . To Prove P equally distant from ...
... extremities of the line . e II . Any point without the perpendicular is un- equally distant from the extremities of the line . 12 D B I. Let CD be to AB at its middle point D , and P be any point on CD . To Prove P equally distant from ...
Σελίδα 22
... extremities of the line . For , by $ 47 , any point on the perpendicular is equally distant from the extremities of the line , and any point without the perpendicular is unequally distant from the extremities of the line . Therefore all ...
... extremities of the line . For , by $ 47 , any point on the perpendicular is equally distant from the extremities of the line , and any point without the perpendicular is unequally distant from the extremities of the line . Therefore all ...
Σελίδα 23
... extremities of another line , the first line is perpendicular to the second at its middle point . Let AB have two of its points m and n each equally distant from the extrem- ities of CD . To Prove AB L to CD at its middle point . Proof ...
... extremities of another line , the first line is perpendicular to the second at its middle point . Let AB have two of its points m and n each equally distant from the extrem- ities of CD . To Prove AB L to CD at its middle point . Proof ...
Σελίδα 25
... extremities of AB ( construction ) . .. CD bisects AB ( § 49 ) . Q.E.F. 56. EXERCISE . Divide a given line into quarters . 57. EXERCISE . If the radius used for describing the two arcs that intersect at C in the figure of Prop . VI is ...
... extremities of AB ( construction ) . .. CD bisects AB ( § 49 ) . Q.E.F. 56. EXERCISE . Divide a given line into quarters . 57. EXERCISE . If the radius used for describing the two arcs that intersect at C in the figure of Prop . VI is ...
Σελίδα 51
... . Suggestion . Use the preceding exercise . 176. EXERCISE . A B The lines AB and CD have their extremities joined by CB and AD . Prove CB + AD > AB + CD . PROPOSITION XXVII . THEOREM 177. If from a point within BOOK I 51.
... . Suggestion . Use the preceding exercise . 176. EXERCISE . A B The lines AB and CD have their extremities joined by CB and AD . Prove CB + AD > AB + CD . PROPOSITION XXVII . THEOREM 177. If from a point within BOOK I 51.
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC AB² ABC and DEF AC² altitude angle formed angles are equal angles equal apothem bisector bisects chord circum circumference cone Construct a triangle COROLLARY cylinder DEFINITION diagonals diameter dihedral angles divided Draw EFGH equally distant equiangular polygon equilateral triangle equivalent EXERCISE exterior angles Find frustum given circle given line given point hypotenuse inscribed angle isosceles triangle joining the middle lateral area Let ABC Let To Prove line joining medians meet middle points number of sides opposite sides parallel parallelogram parallelopiped perimeter perpendicular point of intersection polyhedron prism prolonged PROPOSITION Prove ABCD pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons slant height sphere spherical square straight line surface tangent tetrahedron THEOREM trapezoid triangle ABC trihedral unequal vertex vertical angle volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 167 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 139 - A line parallel to one side of a triangle divides the other two sides proportionally.
Σελίδα 187 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 202 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 180 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Σελίδα 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Σελίδα 195 - Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig.
Σελίδα 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Σελίδα 15 - 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.
Σελίδα 17 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.