Plane and Solid GeometryCentury Company, 1906 - 418 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 100.
Σελίδα xii
... to Professor Leland L. Landers , of the Richmond Hill High School , for valuable suggestions , and for their kindness in reading the proof - sheets . GEOMETRY INTRODUCTION GENERAL TERMS 1 A proposition is the expression xii PREFACE.
... to Professor Leland L. Landers , of the Richmond Hill High School , for valuable suggestions , and for their kindness in reading the proof - sheets . GEOMETRY INTRODUCTION GENERAL TERMS 1 A proposition is the expression xii PREFACE.
Σελίδα 15
... PROOF -C ' Place the ABC on the A'B'C ' so that the vertex B falls on the vertex B ' , and the line BA along the line B'A ' . Then BC will fall along B'C ' . .. the ABC and A'B'C ' coincide and are equal . 101 COROLLARY 1 . All right ...
... PROOF -C ' Place the ABC on the A'B'C ' so that the vertex B falls on the vertex B ' , and the line BA along the line B'A ' . Then BC will fall along B'C ' . .. the ABC and A'B'C ' coincide and are equal . 101 COROLLARY 1 . All right ...
Σελίδα 16
... PROOF ZADB + ADC = the st . △ BDC + ≤ Ax . 13 = 2 rt . s . " A st . is equal to two rt . 4. ” § 70 Q. E. D. 104 COROLLARY 1. The complements of equal angles are equal . 105 COROLLARY 2. The supplements of equal angles are equal . 106 ...
... PROOF ZADB + ADC = the st . △ BDC + ≤ Ax . 13 = 2 rt . s . " A st . is equal to two rt . 4. ” § 70 Q. E. D. 104 COROLLARY 1. The complements of equal angles are equal . 105 COROLLARY 2. The supplements of equal angles are equal . 106 ...
Σελίδα 19
... PROOF Zm is the sup . of △ s , and n is the sup . of △ s . § 103 :: < m = < n . · . < m " The supplements of equal Likewise s = L t . are equal . ” § 105 Q. E. D. EXERCISES * 17 If 21 = 38 ° , find ≤3 , Z4 , 22 . 18 If 3 is four ...
... PROOF Zm is the sup . of △ s , and n is the sup . of △ s . § 103 :: < m = < n . · . < m " The supplements of equal Likewise s = L t . are equal . ” § 105 Q. E. D. EXERCISES * 17 If 21 = 38 ° , find ≤3 , Z4 , 22 . 18 If 3 is four ...
Σελίδα 25
... PROOF Let AB and CD be parallel lines cut by the transversal EF . Then / m = Zp , being vert . s . But r = p by the theorem . • : < m = < r . Z = L § 112 § 121 Ax . 11 Likewise 0 Lt , 2 n = 2 s , ≤ p = L v .. 123 COROLLARY 2. If two ...
... PROOF Let AB and CD be parallel lines cut by the transversal EF . Then / m = Zp , being vert . s . But r = p by the theorem . • : < m = < r . Z = L § 112 § 121 Ax . 11 Likewise 0 Lt , 2 n = 2 s , ≤ p = L v .. 123 COROLLARY 2. If two ...
Περιεχόμενα
3 | |
11 | |
20 | |
30 | |
53 | |
62 | |
68 | |
78 | |
262 | |
268 | |
284 | |
296 | |
303 | |
321 | |
338 | |
344 | |
95 | |
111 | |
125 | |
132 | |
141 | |
192 | |
199 | |
225 | |
239 | |
254 | |
353 | |
365 | |
374 | |
382 | |
389 | |
400 | |
411 | |
416 | |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal arc BC assigned quantity base bisectors bisects chord circumference circumscribed Compute CONCLUSION cone construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equiangular polygon equidistant equilateral triangle exterior angle Find the area Find the locus frustum given circle given line given point homologous hypotenuse HYPOTHESIS inches inscribed intersect isosceles trapezoid isosceles triangle lateral area legs lune median mid-points number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron prism PROOF Draw PROOF Let Prove pyramid Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular polygon rhombus right angles right triangle SCHOLIUM secant segment semicircle spherical angle spherical degrees spherical excess spherical polygon spherical triangle straight line surface symmetrical tangent tetraedron THEOREM trapezoid triangle ABC triedral vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 168 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 41 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 35 - Any side of a triangle is less than the sum of the other two sides...
Σελίδα 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Σελίδα 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Σελίδα 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 199 - Two triangles having 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.
Σελίδα 192 - The areas of two rectangles having equal altitudes are to each other as their bases.
Σελίδα 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...