Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 páginas |
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Página xi
... consequently a new proportion . Let there be , for example , the proportion , we shall have or 4 : 6 : 12 18 , 644 : 18 +12 : 12 , 10 : 4 : 30 : 12 . 2. If from the consequent of a ratio we subtract the antecedent , and compare the ...
... consequently a new proportion . Let there be , for example , the proportion , we shall have or 4 : 6 : 12 18 , 644 : 18 +12 : 12 , 10 : 4 : 30 : 12 . 2. If from the consequent of a ratio we subtract the antecedent , and compare the ...
Página xii
... consequently B + A : D + C :: B - A : D - C , or , by changing the place of the means , BAB - A :: D + C : D - C ; that is , the sum of the two first terms of a proportion is to their dif- ference , as the sum of the two last is to ...
... consequently B + A : D + C :: B - A : D - C , or , by changing the place of the means , BAB - A :: D + C : D - C ; that is , the sum of the two first terms of a proportion is to their dif- ference , as the sum of the two last is to ...
Página 17
... Consequently AB and CD are perpendicu- lar to the same straight line PQ , therefore they are parallel ( 57 ) . L THEOREM . 69. Two parallel lines are throughout at the same distance from each other . Demonstration . The two parallels AB ...
... Consequently AB and CD are perpendicu- lar to the same straight line PQ , therefore they are parallel ( 57 ) . L THEOREM . 69. Two parallel lines are throughout at the same distance from each other . Demonstration . The two parallels AB ...
Página 21
... consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig ...
... consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig ...
Página 27
... consequently the third side CF is equal to the third side CG ; therefore the two equal chords AB , DE , are at the same distance from the centre . 2. Let the chord AH be greater than DE , the arc AKH will be greater than the arc DME ...
... consequently the third side CF is equal to the third side CG ; therefore the two equal chords AB , DE , are at the same distance from the centre . 2. Let the chord AH be greater than DE , the arc AKH will be greater than the arc DME ...
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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...