Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 σελίδες |
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Σελίδα 11
... evidently be isosceles ; and if those lines be likewise equal to the base AB , the triangle must be equilateral . PROP . II . THEOREM . Two triangles are equal , which have all the sides of the one equal to the corresponding sides of ...
... evidently be isosceles ; and if those lines be likewise equal to the base AB , the triangle must be equilateral . PROP . II . THEOREM . Two triangles are equal , which have all the sides of the one equal to the corresponding sides of ...
Σελίδα 18
... evidently greater than DCE , it is con- sequently greater than DBA or ABC . In like manner , it may be shown , that if BC be produced , the exterior angle ACG is greater than CAB . But ACG is equal to its vertical angle BCF ( Def . 10 ...
... evidently greater than DCE , it is con- sequently greater than DBA or ABC . In like manner , it may be shown , that if BC be produced , the exterior angle ACG is greater than CAB . But ACG is equal to its vertical angle BCF ( Def . 10 ...
Σελίδα 49
... evidently complementary rhom- boids , and therefore ( II . 9. ) equivalent ; and by reason of the parallels AE , IF , the angle FID is equal to EAI ( I. 34. ) , which again is equal to BEF or the given angle K. PROP . XII . THEOR . A ...
... evidently complementary rhom- boids , and therefore ( II . 9. ) equivalent ; and by reason of the parallels AE , IF , the angle FID is equal to EAI ( I. 34. ) , which again is equal to BEF or the given angle K. PROP . XII . THEOR . A ...
Σελίδα 51
... . I D K B Again , the parallelograms KB and KE are evidently rectangular ; they are also equal , being contained by equal sides ; and each of them being double of the original tri- 1 angle ACB , they are together equal to the BOOK II . 51.
... . I D K B Again , the parallelograms KB and KE are evidently rectangular ; they are also equal , being contained by equal sides ; and each of them being double of the original tri- 1 angle ACB , they are together equal to the BOOK II . 51.
Σελίδα 57
... evidently meet at the vertex , and consequently the rectangles AB , AN and BC , CP will become the squares of AB and BC . And hence the beautiful Proposition II . 14. is derived , being only a remarkable case of a much more general ...
... evidently meet at the vertex , and consequently the rectangles AB , AN and BC , CP will become the squares of AB and BC . And hence the beautiful Proposition II . 14. is derived , being only a remarkable case of a much more general ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD ANALYSIS angle ABC angle ACB angle BAC bisect centre chord circumference COMPOSITION conse consequently the angle decagon describe a circle diameter distance diverging lines drawn equal to BC exterior angle fall the perpendicular given angle given circle given in position given point given ratio given space given straight line greater hence hypotenuse inflected inscribed intercepted intersection isosceles triangle join let fall mean proportional parallel perpendicular point F polygon porism PROB PROP quently radius rectangle rectangle contained regular polygon rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sequently side AC similar sine square of AB square of AC tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Δημοφιλή αποσπάσματα
Σελίδα 28 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Σελίδα 92 - THE angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same
Σελίδα 458 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 99 - ... a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.
Σελίδα 155 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Σελίδα 408 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Σελίδα 16 - PROP. V. THEOR. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC, be produced to D and E: the angle ABC shall be equal to the angle ACB, and the angle...
Σελίδα 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 60 - Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines.