Elements of GeometryGinn, Heath, & Company, 1879 - 250 σελίδες |
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Σελίδα vi
... take the constant 60 and the repetend .3333 , etc. , the approxi- mate values of the repetend will be 1 % , 10 % , 1800 , 3333 , etc. , and these values multiplied by 60 give the series 18 , 19.8 , 19.98 , 19.998 , etc. , which ...
... take the constant 60 and the repetend .3333 , etc. , the approxi- mate values of the repetend will be 1 % , 10 % , 1800 , 3333 , etc. , and these values multiplied by 60 give the series 18 , 19.8 , 19.98 , 19.998 , etc. , which ...
Σελίδα 12
... take the position AED , and the angles DEF and ABC will together equal the an- gle A EF . B D A F C D A E MATHEMATICAL TERMS . 36. DEF . A Demonstration is a course of reasoning by which the truth or falsity of a particular statement is ...
... take the position AED , and the angles DEF and ABC will together equal the an- gle A EF . B D A F C D A E MATHEMATICAL TERMS . 36. DEF . A Demonstration is a course of reasoning by which the truth or falsity of a particular statement is ...
Σελίδα 15
... Take away from each of these equals the common ≤ OC A. Then = LOCB LACP . In like manner we may prove = ZACO Z PCB . Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of ...
... Take away from each of these equals the common ≤ OC A. Then = LOCB LACP . In like manner we may prove = ZACO Z PCB . Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of ...
Σελίδα 16
... Take away from each of these equals the common △ O C A. Then = LOCF ZOC B. .. C B and C F coincide , and cannot form two lines as rep- resented in the figure . .. A C and C B are in the same straight line . Q. E. D. PROPOSITION III ...
... Take away from each of these equals the common △ O C A. Then = LOCF ZOC B. .. C B and C F coincide , and cannot form two lines as rep- resented in the figure . .. A C and C B are in the same straight line . Q. E. D. PROPOSITION III ...
Σελίδα 17
... take the direction of O E , ( since LCOF = LEOF , each being a rt . 4 ) . The point C will fall upon the point E , ( since OCOE by cons . ) . .. line CF : = line FE , ( having their extremities in the same points ) . ..CFFE = 2 CF , CO ...
... take the direction of O E , ( since LCOF = LEOF , each being a rt . 4 ) . The point C will fall upon the point E , ( since OCOE by cons . ) . .. line CF : = line FE , ( having their extremities in the same points ) . ..CFFE = 2 CF , CO ...
Άλλες εκδόσεις - Προβολή όλων
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.