Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 páginas |
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Página 29
... drawn through the point F paral- lel to AB , it follows that the converse of the proposition is true , and that those ... draw , through the point C , a straight line parallel to AB . In AB take any point D , join CD , and at the point C ...
... drawn through the point F paral- lel to AB , it follows that the converse of the proposition is true , and that those ... draw , through the point C , a straight line parallel to AB . In AB take any point D , join CD , and at the point C ...
Página 37
... draw a perpendicular from the extremity of a given straight line . From the point B , to draw a perpendicular to AB , with◅ out producing that line . In AB take any point C , and on BC ( I. 1. cor . ) describe an equilateral triangle ...
... draw a perpendicular from the extremity of a given straight line . From the point B , to draw a perpendicular to AB , with◅ out producing that line . In AB take any point C , and on BC ( I. 1. cor . ) describe an equilateral triangle ...
Página 39
... draw a straight line AC in which take the portion AD , and repeat it five times from A to C , join CB , and from the several points of section D , E , F , and G draw the pa- rallels DH , EI , FK , and GL , ( I. 26. ) cutting AB in H , I ...
... draw a straight line AC in which take the portion AD , and repeat it five times from A to C , join CB , and from the several points of section D , E , F , and G draw the pa- rallels DH , EI , FK , and GL , ( I. 26. ) cutting AB in H , I ...
Página 42
... draw AE ( I. 26. ) parallel to CB , and from C draw CF parallel to AD . E B D Because the triangles ABC , ADC have the same alti- tude , the straight line EF is parallel to AC ( I. 27. ) , and consequently the figures CE and AF are ...
... draw AE ( I. 26. ) parallel to CB , and from C draw CF parallel to AD . E B D Because the triangles ABC , ADC have the same alti- tude , the straight line EF is parallel to AC ( I. 27. ) , and consequently the figures CE and AF are ...
Página 43
... draw AG and DH parallel to CB and FE ( I. 26. ) , and join AH , CE . Because the triangles ABC , DEF are of equal altitude , GE is parallel to AF ( I. 27. ) , and B H GC , HF are parallelograms . But C AC , being equal to DF , and DF ...
... draw AG and DH parallel to CB and FE ( I. 26. ) , and join AH , CE . Because the triangles ABC , DEF are of equal altitude , GE is parallel to AF ( I. 27. ) , and B H GC , HF are parallelograms . But C AC , being equal to DF , and DF ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Página 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
Página 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...
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.