Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 sider |
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Side 11
... sequently the triangle ACB answers the conditions of the problem . Corollary . If the radii G and H be equal to each other , the triangle will evidently be isosceles ; and if those lines be likewise equal to the base AB , the triangle ...
... sequently the triangle ACB answers the conditions of the problem . Corollary . If the radii G and H be equal to each other , the triangle will evidently be isosceles ; and if those lines be likewise equal to the base AB , the triangle ...
Side 17
... sequently those sides must be equal . Cor . Every equiangular triangle is also equilateral . PROP . X. THEOR . The exterior angle of a triangle is greater than either of the interior opposite angles . The exterior angle BCF , formed by ...
... sequently those sides must be equal . Cor . Every equiangular triangle is also equilateral . PROP . X. THEOR . The exterior angle of a triangle is greater than either of the interior opposite angles . The exterior angle BCF , formed by ...
Side 18
... 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. ) , and hence BCF must be greater than ...
... 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. ) , and hence BCF must be greater than ...
Side 19
... sequently ( I. 10. ) greater than the opposite interior angle CED . ADE B If the line CD be , therefore , supposed to turn about the point C in the direction of AB , the angle which it makes with the intercepted part of the line from A ...
... sequently ( I. 10. ) greater than the opposite interior angle CED . ADE B If the line CD be , therefore , supposed to turn about the point C in the direction of AB , the angle which it makes with the intercepted part of the line from A ...
Side 24
... sequently the opposite angle IBH of the triangle BIH is ( I. 14. ) greater than BHI . But AB being equal to AH the angle HBA is ( I. 8. ) equal to BHA , and therefore the two angles IBH and HBA are greater than IHB and BHA , that is ...
... sequently the opposite angle IBH of the triangle BIH is ( I. 14. ) greater than BHI . But AB being equal to AH the angle HBA is ( I. 8. ) equal to BHA , and therefore the two angles IBH and HBA are greater than IHB and BHA , that is ...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Side 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
Side 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...
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.