Elements of GeometryGinn, Heath, & Company, 1879 - 250 σελίδες |
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Σελίδα 45
George Albert Wentworth. PROPOSITION XXVI . THEOREM . 109. Two right triangles are equal when a side and the hypotenuse of the one are equal respectively to a side and the hypotenuse of the other . A B Α ' A C B C In the right triangles ...
George Albert Wentworth. PROPOSITION XXVI . THEOREM . 109. Two right triangles are equal when a side and the hypotenuse of the one are equal respectively to a side and the hypotenuse of the other . A B Α ' A C B C In the right triangles ...
Σελίδα 46
... equal respectively to the hypotenuse and an acute angle of the other . B A B Α ' CI In the right triangles A B C and ... equal to an acute then the other acute & are equal ) . - .. ΔΑΒΟ △ A'B'C ' , ( two are equal when a side and two ...
... equal respectively to the hypotenuse and an acute angle of the other . B A B Α ' CI In the right triangles A B C and ... equal to an acute then the other acute & are equal ) . - .. ΔΑΒΟ △ A'B'C ' , ( two are equal when a side and two ...
Σελίδα 47
... equal sides are equal . C We Leary to prove 1 = 7 Y E B 2 W Let A BG be an isosceles triangle , having the sides AC ... respectively to two sides and the included ..LA = LB , ( being homologous △ of equal △ ) . Hyp . Iden . Cons ...
... equal sides are equal . C We Leary to prove 1 = 7 Y E B 2 W Let A BG be an isosceles triangle , having the sides AC ... respectively to two sides and the included ..LA = LB , ( being homologous △ of equal △ ) . Hyp . Iden . Cons ...
Σελίδα 48
... equal respectively to two sides and the included of the other ) . Also , II . ZCEA = LCEB , ( being homologous & of equal △ ) . .. CE is to A B , ( a straight line meeting another , making the adjacent equal , is to Also , III . that ...
... equal respectively to two sides and the included of the other ) . Also , II . ZCEA = LCEB , ( being homologous & of equal △ ) . .. CE is to A B , ( a straight line meeting another , making the adjacent equal , is to Also , III . that ...
Σελίδα 49
... equal respectively to a side and an acute of the other ) . .. A B = AC , ( being homologous sides of equal △ ) . Q. E. D. Ex . Show that an equiangular triangle is also equilateral . A PROPOSITION XXXI . THEOREM . 115. If two triangles ...
... equal respectively to a side and an acute of the other ) . .. A B = AC , ( being homologous sides of equal △ ) . Q. E. D. Ex . Show that an equiangular triangle is also equilateral . A PROPOSITION XXXI . THEOREM . 115. If two triangles ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A B C AABC AACB ABCD acute adjacent angles alt.-int altitude arc A B base bisect centre circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon exterior angles figure Geometry given circle given line given point given straight line greater homologous sides hypotenuse Iden isosceles triangle Let A B limit line A B measured by arc middle point number of sides parallelogram perimeter perpendicular PHILLIPS EXETER ACADEMY plane PROBLEM prove Q. E. D. PROPOSITION quadrilateral quantities radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct rhombus right angles right triangle SCHOLIUM segment shortest side sides of equal similar polygons subtend tangent THEOREM third side triangle ABC variable vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 144 - The areas of two triangles which have 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 38 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 134 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 200 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 173 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 159 - In any triangle the product of two sides is equal to the product of the diameter...
Σελίδα 132 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 70 - I) is a parallelogram, E and F the middle points of AD and BC respectively ; show that BE and DF will trisect the diagonal A C.
Σελίδα 48 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...
Σελίδα 81 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.