Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 85.
Σελίδα v
... on each step . After a Book has been read in this way the pupil should review the Book , and should be required to draw the figures free - hand . He should state and prove the propositions orally , using a PREFACE . V.
... on each step . After a Book has been read in this way the pupil should review the Book , and should be required to draw the figures free - hand . He should state and prove the propositions orally , using a PREFACE . V.
Σελίδα 15
... prove = LOCB LACP . = = rt . , LOCA + Z OCB 2 rt . 4 , ( being sup . - adj . 4 ) . = LOCA + ZACP 2 rt . 4 , ( being sup . - adj . ) . .LOCA + ZOCB = LOCA + ZACP . § 34 § 34 Ax . 1 . Take away from each of these equals the common ≤ O C ...
... prove = LOCB LACP . = = rt . , LOCA + Z OCB 2 rt . 4 , ( being sup . - adj . 4 ) . = LOCA + ZACP 2 rt . 4 , ( being sup . - adj . ) . .LOCA + ZOCB = LOCA + ZACP . § 34 § 34 Ax . 1 . Take away from each of these equals the common ≤ O C ...
Σελίδα 16
... prove A C and C B in the same straight line . Suppose C F to be in the same straight line with A C. Then = LOCA + ZOCF 2 rt . . ( being sup . - adj . ) . s . $ 34 But Hyp . ..LOCA + ZOCF : - LOC A + Z OC B. Ax . 1 . = ZOCA + Z OCB 2 rt ...
... prove A C and C B in the same straight line . Suppose C F to be in the same straight line with A C. Then = LOCA + ZOCF 2 rt . . ( being sup . - adj . ) . s . $ 34 But Hyp . ..LOCA + ZOCF : - LOC A + Z OC B. Ax . 1 . = ZOCA + Z OCB 2 rt ...
Σελίδα 17
... prove CO < any other line drawn from C to A B , as CF. Produce CO to E , making O E Draw EF . - CO . On A B as an axis , fold over OCF until it comes into the plane of O E F. The line OC will take the direction of O E , ( since CO F ...
... prove CO < any other line drawn from C to A B , as CF. Produce CO to E , making O E Draw EF . - CO . On A B as an axis , fold over OCF until it comes into the plane of O E F. The line OC will take the direction of O E , ( since CO F ...
Σελίδα 20
... prove CH > CK . Produce CF to E , making F E = C F. Draw EK and EH . CH = HE , and CK = KE , $ 53 ( two oblique lines drawn from the same point in a 1 , cutting off equal dis- tances from the foot of the 1 , are equal ) . But CHHECK + ...
... prove CH > CK . Produce CF to E , making F E = C F. Draw EK and EH . CH = HE , and CK = KE , $ 53 ( two oblique lines drawn from the same point in a 1 , cutting off equal dis- tances from the foot of the 1 , are equal ) . But CHHECK + ...
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'.