Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 páginas |
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Página 14
... preceding case , that the point M can neither fall upon G nor upon any point in the direction GA , so that the distance AM will be necessarily greater than AG . It may be observed , moreover , that if the figure is constructed with care ...
... preceding case , that the point M can neither fall upon G nor upon any point in the direction GA , so that the distance AM will be necessarily greater than AG . It may be observed , moreover , that if the figure is constructed with care ...
Página 31
... preceding theorem , angle ACB : angle ACI :: arc AB : arc AI . Comparing these two proportions together , and observing , that the antecedents are the same , we conclude that the consc- quents are proportional ( 111 ) † , namely , angle ...
... preceding theorem , angle ACB : angle ACI :: arc AB : arc AI . Comparing these two proportions together , and observing , that the antecedents are the same , we conclude that the consc- quents are proportional ( 111 ) † , namely , angle ...
Página 32
... preceding propositions . 124. Scholium . It may seem more natural to measure a quan- tity by another quantity of the same kind , and upon this princi- ple it would be convenient to refer all angles to the right angle ; and thus , the ...
... preceding propositions . 124. Scholium . It may seem more natural to measure a quan- tity by another quantity of the same kind , and upon this princi- ple it would be convenient to refer all angles to the right angle ; and thus , the ...
Página 41
... preceding . This last remainder will be the common measure of the two proposed lines ; and , by regarding it as unity , the values of the preceding remainders are easily found , and , at length , those of the proposed lines , from which ...
... preceding . This last remainder will be the common measure of the two proposed lines ; and , by regarding it as unity , the values of the preceding remainders are easily found , and , at length , those of the proposed lines , from which ...
Página 42
... preceding prob- lem ; for an arc may be applied to an arc of the same radius , as a straight line is applied to a straight line . We shall thus obtain a common measure of the arcs CD , EF , if they have one , and their ratio in numbers ...
... preceding prob- lem ; for an arc may be applied to an arc of the same radius , as a straight line is applied to a straight line . We shall thus obtain a common measure of the arcs CD , EF , if they have one , and their ratio in numbers ...
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Términos y frases comunes
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Pasajes populares
Página 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 7 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Página 76 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Página 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Página 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Página 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Página 203 - In every triangle the sum of the three angles is equal to two right angles.
Página 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Página 141 - If a pyramid is cut by a plane parallel to its base, the...