Elements of Plane and Solid GeometryAmerican Book Company, 1903 - 384 σελίδες |
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Σελίδα 13
... prolonged to any length . 3. If two lines are unequal , the length of the smaller can be laid off on the larger . 4. A circumference can be described with any point as a center , and with a radius of any length . SYMBOLS AND ...
... prolonged to any length . 3. If two lines are unequal , the length of the smaller can be laid off on the larger . 4. A circumference can be described with any point as a center , and with a radius of any length . SYMBOLS AND ...
Σελίδα 27
... Prolong one of the lines , as OE , to G. Then apply § 63 to the angles on each side of GE . 65. DEFINITION . If two angles are together equal to two right angles , they are called supplemen- tary angles . Each angle is the sup- plement ...
... Prolong one of the lines , as OE , to G. Then apply § 63 to the angles on each side of GE . 65. DEFINITION . If two angles are together equal to two right angles , they are called supplemen- tary angles . Each angle is the sup- plement ...
Σελίδα 33
... Prolong CD until DF = CD , and draw EF . Prove CDE and FDE equal in all respects . Whence 21 = 22 . But ≤11 R.A. by supposition . Show that 21 + 22 = 2 R.A.'s . If the sum of angles 1 and 2 is two R.A.'s , CE and EF form a straight ...
... Prolong CD until DF = CD , and draw EF . Prove CDE and FDE equal in all respects . Whence 21 = 22 . But ≤11 R.A. by supposition . Show that 21 + 22 = 2 R.A.'s . If the sum of angles 1 and 2 is two R.A.'s , CE and EF form a straight ...
Σελίδα 36
... prolonged . PROPOSITION XVI . THEOREM 108. If two lines are parallel to a third line , they are parallel to each other . A C E- Let AB and CD be to EF . To Prove AB and CD to each other . -F Proof . Since AB and CD are in the same plane ...
... prolonged . PROPOSITION XVI . THEOREM 108. If two lines are parallel to a third line , they are parallel to each other . A C E- Let AB and CD be to EF . To Prove AB and CD to each other . -F Proof . Since AB and CD are in the same plane ...
Σελίδα 39
... prolong MH until it meets AB in some point G. Prove the AGMO and MSH equal in all respects . Whence < H = ZG . LH is by construction a R.A. .. G is a R.A. AB and CD are parallel . ( ? ) Q.E.D. 116. COROLLARY . If two lines are cut by a ...
... prolong MH until it meets AB in some point G. Prove the AGMO and MSH equal in all respects . Whence < H = ZG . LH is by construction a R.A. .. G is a R.A. AB and CD are parallel . ( ? ) Q.E.D. 116. COROLLARY . If two lines are cut by a ...
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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.