Euclid's Elements of geometry, the first three books (the fourth, fifth, and sixth books) tr. from the Lat. To which is added, A compendium of algebra (A compendium of trigonometry).1846 |
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Seite 61
... quotient CF , from the square of the remaining side CB , and the square root , BF , of the residue , multiplied into half the former divisor AC , gives the area of the triangle . COR . If from any angle ( A ) of a triangle ( BAP , ) a ...
... quotient CF , from the square of the remaining side CB , and the square root , BF , of the residue , multiplied into half the former divisor AC , gives the area of the triangle . COR . If from any angle ( A ) of a triangle ( BAP , ) a ...
Seite 105
... quotient , as we find them in the dividend . = a3 , because by subtracting the index Ex . gr .: a4 a of the divisor from that of the dividend , there will remain for the quotient , a3 ; and a2d3 a = ad3 ; it is also to be understood ...
... quotient , as we find them in the dividend . = a3 , because by subtracting the index Ex . gr .: a4 a of the divisor from that of the dividend , there will remain for the quotient , a3 ; and a2d3 a = ad3 ; it is also to be understood ...
Seite 106
... quotient is to be found by dividing by that quantity , and noting down the unlike quantities as found in the dividend ; therefore , 10ad- a produces 10d , which is evident from the following numerical proof ; -suppose a = 4 , and d = 6 ...
... quotient is to be found by dividing by that quantity , and noting down the unlike quantities as found in the dividend ; therefore , 10ad- a produces 10d , which is evident from the following numerical proof ; -suppose a = 4 , and d = 6 ...
Seite 107
... quotient . We next multiply the whole divisor by the quotient thus found , and subtract the result from the dividend , for a new dividend ; bringing down other terms , when required , if any . Should there be a remainder not divisible ...
... quotient . We next multiply the whole divisor by the quotient thus found , and subtract the result from the dividend , for a new dividend ; bringing down other terms , when required , if any . Should there be a remainder not divisible ...
Seite 110
... quotient and the first term of the divisor is then to be divided into its co - efficient , namely , into ab2 , placing the result also in the quotient , and proceed as usual , by multiplying ( n - 1 ) ab ; then subtract the product , b ...
... quotient and the first term of the divisor is then to be divided into its co - efficient , namely , into ab2 , placing the result also in the quotient , and proceed as usual , by multiplying ( n - 1 ) ab ; then subtract the product , b ...
Häufige Begriffe und Wortgruppen
absurd AC and CB AC by Prop AC is equal angle ABC angle equal angles by Prop arch bisected centre circumference co-efficient Const construct contained oftener diameter divided divisor double equal angles equal by Constr equal by Hypoth equal by Prop equal right lines equal to AC equal to twice equi-multiples equi-submultiples equiangular equilateral external angle fore fraction given angle given circle given line given right line given triangle greater half a right inscribed less multiplied opposite parallel parallelogram perpendicular PROPOSITION quantities quotient ratio rectangle under AC remaining angles remaining side right angle right line AB right line AC SCHOL segment semicircle side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle twice the square whole
Beliebte Passagen
Seite 20 - If two triangles have two sides of the one equal to two sides of the...
Seite 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 209 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Seite 218 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 114 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Seite 90 - 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.
Seite 129 - In any proportion, the product of the means is equal to the product of the extremes.
Seite 163 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Seite 215 - ... are to one another in the duplicate ratio of their homologous sides.
Seite 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.