Elements of Plane GeometryAmerican Book Company, 1901 - 247 σελίδες |
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Σελίδα 131
... consequent with consequent . If the proportion α b d comes - = 1 с a = C d is arranged by alternation , it be- PROPOSITION III . THEOREM 417. If four quantities are in proportion , they are in proportion by alternation . Let To Prove a ...
... consequent with consequent . If the proportion α b d comes - = 1 с a = C d is arranged by alternation , it be- PROPOSITION III . THEOREM 417. If four quantities are in proportion , they are in proportion by alternation . Let To Prove a ...
Σελίδα 132
... consequent is compared with either antecedent or consequent . The proportion a с - = - b d a + b α = arranged by composition becomes c + d or a + b c + d = · с b d PROPOSITION V. THEOREM 422. If four quantities are in proportion , they ...
... consequent is compared with either antecedent or consequent . The proportion a с - = - b d a + b α = arranged by composition becomes c + d or a + b c + d = · с b d PROPOSITION V. THEOREM 422. If four quantities are in proportion , they ...
Σελίδα 133
... consequent is com- pared with either antecedent or consequent . The proportion a b c - d or a с a a b - b = b с arranged by division becomes d - a d с d b d or а - b с — с or α b d - c d PROPOSITION VI . THEOREM 428. If four quantities ...
... consequent is com- pared with either antecedent or consequent . The proportion a b c - d or a с a a b - b = b с arranged by division becomes d - a d с d b d or а - b с — с or α b d - c d PROPOSITION VI . THEOREM 428. If four quantities ...
Σελίδα 134
... consequent is compared with the difference of antecedent and consequent . a с The proportion = arranged by composition and division , becomes ď a + b а b - = c + d с d PROPOSITION VII . THEOREM 431. If four quantities are in 134 PLANE ...
... consequent is compared with the difference of antecedent and consequent . a с The proportion = arranged by composition and division , becomes ď a + b а b - = c + d с d PROPOSITION VII . THEOREM 431. If four quantities are in 134 PLANE ...
Σελίδα 137
... consequent . Let To Prove Proof α a e 9 . 1-2-3-4- d f h a + c + e + g e b + d + f + h ; - ; ( 2 ) - d ( 3 ) 9-3 ( 4 ) 9 h - ( 5 ) af be ( 6 ) = = f From ( 1 ) . ef = de ( 7 ) From ( 2 ) , ( 3 ) , ( 4 ) , and ( 5 ) . ef = fe ( 8 ) gf = he ...
... consequent . Let To Prove Proof α a e 9 . 1-2-3-4- d f h a + c + e + g e b + d + f + h ; - ; ( 2 ) - d ( 3 ) 9-3 ( 4 ) 9 h - ( 5 ) af be ( 6 ) = = f From ( 1 ) . ef = de ( 7 ) From ( 2 ) , ( 3 ) , ( 4 ) , and ( 5 ) . ef = fe ( 8 ) gf = he ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc ABC arcs intercepted BC² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point homologous homologous sides hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ΔΑΒΟ ᎠᏴ
Δημοφιλή αποσπάσματα
Σελίδα 68 - 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.
Σελίδα 163 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
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 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.
Σελίδα 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Σελίδα 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
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 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Σελίδα 11 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Σελίδα 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.