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 156
... proportion , D = nq.c = q.nc = qC . PROP . VI . THEOR . If four numbers be proportional , the product of the extremes is equal to that of the means ; and of two equal products , the factors are convertible into an analogy , of which ...
... proportion , D = nq.c = q.nc = qC . PROP . VI . THEOR . If four numbers be proportional , the product of the extremes is equal to that of the means ; and of two equal products , the factors are convertible into an analogy , of which ...
Página 157
... means . Cor . 2. Hence also a proportion is not affected , by trans- posing or interchanging its extreme and mean terms . On this principle , is founded the two following theorems . PROP . VII . THEOR . The terms of an analogy are ...
... means . Cor . 2. Hence also a proportion is not affected , by trans- posing or interchanging its extreme and mean terms . On this principle , is founded the two following theorems . PROP . VII . THEOR . The terms of an analogy are ...
Página 158
... mean terms , A + B : B :: C + D : D . PROP . X. THEOR . The terms of an analogy are proportional by divi- sion ; or the difference of the first and second is to the second , as the difference of the third and fourth to the fourth . Let ...
... mean terms , A + B : B :: C + D : D . PROP . X. THEOR . The terms of an analogy are proportional by divi- sion ; or the difference of the first and second is to the second , as the difference of the third and fourth to the fourth . Let ...
Página 181
... mean terms B and C be equal , it is obvious , that DG will become equal to DF , and that DH will be found a third proportional to the two given terms A and B. PROP . IV . PROB . To cut a given straight line into segments which shall be ...
... mean terms B and C be equal , it is obvious , that DG will become equal to DF , and that DH will be found a third proportional to the two given terms A and B. PROP . IV . PROB . To cut a given straight line into segments which shall be ...
Página 185
... mean pro- portional between the distances of the middle from the two points ... proportional between EC and ED , or EC : EB :: EB : ED . E C B D For since ... proportion . Let the diverging lines EA , EC , EB , and ED terminate in the ...
... mean pro- portional between the distances of the middle from the two points ... proportional between EC and ED , or EC : EB :: EB : ED . E C B D For since ... proportion . Let the diverging lines EA , EC , EB , and ED terminate in the ...
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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.