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 |
Inni boken
Resultat 1-5 av 17
Side 36
... difference between two given rectilineal figures , can be found , by applying parallelograms equal to both , to the same right line , and in the same angle , for the difference of these will be a parallelogram , equal to the given ...
... difference between two given rectilineal figures , can be found , by applying parallelograms equal to both , to the same right line , and in the same angle , for the difference of these will be a parallelogram , equal to the given ...
Side 38
... difference of the squares of the given lines , according as the given sides be about the right angle , or not ; if about it , take the sum , if not , take the difference . COR . 2. - Given any number of squares , to find a square equal ...
... difference of the squares of the given lines , according as the given sides be about the right angle , or not ; if about it , take the sum , if not , take the difference . COR . 2. - Given any number of squares , to find a square equal ...
Side 39
... difference of the squares of the segments , AD and DC , of the side on which the perpendicular falls . For the ... difference of the squares of AB and BC , is equal to the difference between the sum of the squares of AD and DB , and the ...
... difference of the squares of the segments , AD and DC , of the side on which the perpendicular falls . For the ... difference of the squares of AB and BC , is equal to the difference between the sum of the squares of AD and DB , and the ...
Side 42
... difference or that which remains in taking b from a ; in the same way a -b + c , or a + c -b , signifies that a and c ought to be joined together , and that bought to be taken from the whole . - 5. The sign indicates multiplication ...
... difference or that which remains in taking b from a ; in the same way a -b + c , or a + c -b , signifies that a and c ought to be joined together , and that bought to be taken from the whole . - 5. The sign indicates multiplication ...
Side 51
... difference . SCHOL . Hence it appears that in a right angled triangle , the rectangle under the sum and difference of the hypothenuse and one side , is equal to the square of the remaining side . COR . 4. The difference of the squares ...
... difference . SCHOL . Hence it appears that in a right angled triangle , the rectangle under the sum and difference of the hypothenuse and one side , is equal to the square of the remaining side . COR . 4. The difference of the squares ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 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.
Side 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.
Side 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.
Side 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.
Side 129 - In any proportion, the product of the means is equal to the product of the extremes.
Side 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.
Side 215 - ... are to one another in the duplicate ratio of their homologous sides.
Side 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.