Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Αποτελέσματα 11 - 15 από τα 24.
Σελίδα 193
... square roots of their areas . Let S and S ' represent the areas of the two similar polygons A B C , etc. , and A'B'C ' , etc. , respectively . Then S : S ' : : A B2 : A ' B22 , ( similar polygons are to each other as the squares of ...
... square roots of their areas . Let S and S ' represent the areas of the two similar polygons A B C , etc. , and A'B'C ' , etc. , respectively . Then S : S ' : : A B2 : A ' B22 , ( similar polygons are to each other as the squares of ...
Σελίδα 194
... square equivalent to the sum of two given squares . B R R A S Let R and R ' be two given squares . It is required to construct a square = R + R ' . Construct the rt . A. Take A B equal to a side of R , and AC equal to a side of R ...
... square equivalent to the sum of two given squares . B R R A S Let R and R ' be two given squares . It is required to construct a square = R + R ' . Construct the rt . A. Take A B equal to a side of R , and AC equal to a side of R ...
Σελίδα 195
... square and R ' the larger . It is required to construct a square = RR . Construct the rt . A. Take A B equal to a side of R. From B as a centre , with a radius equal to a side of R ' , describe an arc cutting the line A X at C. Then AC ...
... square and R ' the larger . It is required to construct a square = RR . Construct the rt . A. Take A B equal to a side of R. From B as a centre , with a radius equal to a side of R ' , describe an arc cutting the line A X at C. Then AC ...
Σελίδα 196
... square required . BH2 = F H2 + BF2 , For 9 = F H2 + E F2 + E B2 , = F II2 + ' E F2 + E C2 + C B2 , = 2 FH2 + EF2 + EC2 + CA2 + AB2 , § 331 ( the sum of the squares on two sides of a rt . A is equivalent to the square on the hypotenuse ) ...
... square required . BH2 = F H2 + BF2 , For 9 = F H2 + E F2 + E B2 , = F II2 + ' E F2 + E C2 + C B2 , = 2 FH2 + EF2 + EC2 + CA2 + AB2 , § 331 ( the sum of the squares on two sides of a rt . A is equivalent to the square on the hypotenuse ) ...
Σελίδα 199
... in the line KD || to the base . $ 325 In like manner we may continue to reduce the number of sides of the polygon until we obtain the △ CIK . Q. E. F. PROPOSITION XXII . PROBLEM . 352. To construct a square CONSTRUCTIONS . 199.
... in the line KD || to the base . $ 325 In like manner we may continue to reduce the number of sides of the polygon until we obtain the △ CIK . Q. E. F. PROPOSITION XXII . PROBLEM . 352. To construct a square CONSTRUCTIONS . 199.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 40 - 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 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Σελίδα 202 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Σελίδα 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 146 - 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'.