Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα 53
... If the angles ABC and ACB , at the base of an isosceles triangle , be bisected by the straight lines BD , CD , show that D B C will be an isosceles triangle . PROPOSITION XXXV . THEOREM . 119. The three bisectors of TRIANGLES . 53.
... If the angles ABC and ACB , at the base of an isosceles triangle , be bisected by the straight lines BD , CD , show that D B C will be an isosceles triangle . PROPOSITION XXXV . THEOREM . 119. The three bisectors of TRIANGLES . 53.
Σελίδα 71
... less two , or , = - 2 n rt . . 2 n rt . 2 rt . 2 rt . , . the exterior - 4 2 rt . taken taken as many times as the ( n - 2 ) , 4 rt . s . = 4 rt . . Q. E. D. EXERCISES . 1. Show that the sum of the interior POLYGONS . 71.
... less two , or , = - 2 n rt . . 2 n rt . 2 rt . 2 rt . , . the exterior - 4 2 rt . taken taken as many times as the ( n - 2 ) , 4 rt . s . = 4 rt . . Q. E. D. EXERCISES . 1. Show that the sum of the interior POLYGONS . 71.
Σελίδα 72
... Show that each angle of an equiangular pentagon is of a right angle . 3. How many sides has an equiangular polygon ... show that BD is equal to A D. 9. If a straight line drawn parallel to the base of a triangle bisect one of the sides ...
... Show that each angle of an equiangular pentagon is of a right angle . 3. How many sides has an equiangular polygon ... show that BD is equal to A D. 9. If a straight line drawn parallel to the base of a triangle bisect one of the sides ...
Σελίδα 84
... Show that , of all straight lines drawn from a point without a circle to the circumference , the least is that which , when produced , passes through the centre . Ex . 2. Show that , of all straight lines drawn from a point within or ...
... Show that , of all straight lines drawn from a point without a circle to the circumference , the least is that which , when produced , passes through the centre . Ex . 2. Show that , of all straight lines drawn from a point within or ...
Σελίδα 85
... base of an isosceles triangle whose vertex C is without the circle , and whose equal sides meet the circle in D and E. Show that CD is equal to CE , ON MEASUREMENT . 190. DEF . To measure a quantity STRAIGHT LINES AND CIRCLES . 85.
... base of an isosceles triangle whose vertex C is without the circle , and whose equal sides meet the circle in D and E. Show that CD is equal to CE , ON MEASUREMENT . 190. DEF . To measure a quantity STRAIGHT LINES AND CIRCLES . 85.
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'.