Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Αποτελέσματα 6 - 10 από τα 13.
Σελίδα 168
... mean proportional between two given H m n E B C Let the two given lines be m and n . It is required to find a mean proportional between m and n . On the straight line A E take A C = m , and CB = n . On A B as a diameter describe a semi ...
... mean proportional between two given H m n E B C Let the two given lines be m and n . It is required to find a mean proportional between m and n . On the straight line A E take A C = m , and CB = n . On A B as a diameter describe a semi ...
Σελίδα 169
... straight line is said to be divided in extreme and mean ratio , when the whole line is to the greater segment as the greater segment is to the less . PROPOSITION XXVII . PROBLEM . 311. To divide a given CONSTRUCTIONS . 169.
... straight line is said to be divided in extreme and mean ratio , when the whole line is to the greater segment as the greater segment is to the less . PROPOSITION XXVII . PROBLEM . 311. To divide a given CONSTRUCTIONS . 169.
Σελίδα 170
... mean ratio . A E H B D Let A B be the given line . It is required to divide A B in extreme and mean ratio . At B erect a BC , equal to one - half of A B. From C as a centre , with a radius equal to C B , describe a O. Since AB is to the ...
... mean ratio . A E H B D Let A B be the given line . It is required to divide A B in extreme and mean ratio . At B erect a BC , equal to one - half of A B. From C as a centre , with a radius equal to C B , describe a O. Since AB is to the ...
Σελίδα 171
... mean ratio . Cons . Ax . 1 § 263 Q. E. F. REMARK . AB is said to be divided at H , internally , in extreme and mean ratio . If BA be produced to H ' , making A H ' equal to A D , A B is said to be divided at H ' , externally , in ...
... mean ratio . Cons . Ax . 1 § 263 Q. E. F. REMARK . AB is said to be divided at H , internally , in extreme and mean ratio . If BA be produced to H ' , making A H ' equal to A D , A B is said to be divided at H ' , externally , in ...
Σελίδα 202
... mean proportional between the segments of the diameter ) . .. N p2 = MNX NO = a xb , $ 259 ( the product of the means is equal to the product of the extremes ) . Q. E. F. 355. COROLLARY 1. A square may be constructed equiva- lent to a ...
... mean proportional between the segments of the diameter ) . .. N p2 = MNX NO = a xb , $ 259 ( the product of the means is equal to the product of the extremes ) . Q. E. F. 355. COROLLARY 1. A square may be constructed equiva- lent to a ...
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'.