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 27
Side 47
... rectangle is found , by multiplying the altitude into the base ; and from Prop . 35 and 36 , B. 1 , the area of any ... under the whole line , ( AB , ) and each of the parts , ( AC , CB . ) For , on AB describe the square ADEF , ( by Prop .
... rectangle is found , by multiplying the altitude into the base ; and from Prop . 35 and 36 , B. 1 , the area of any ... under the whole line , ( AB , ) and each of the parts , ( AC , CB . ) For , on AB describe the square ADEF , ( by Prop .
Side 48
... rectangle CE is the rectangle under AC and CB , for CF is equal to AC , ( by Const . , and Defin . 31 , B. 1. ) OTHERWISE . Assume a right line X , equal to AC . The rectangles under X and AF , is equal to sum of the rectangles under X and ...
... rectangle CE is the rectangle under AC and CB , for CF is equal to AC , ( by Const . , and Defin . 31 , B. 1. ) OTHERWISE . Assume a right line X , equal to AC . The rectangles under X and AF , is equal to sum of the rectangles under X and ...
Side 49
... rectangle under the parts . OTHERWISE . The square of AB is equal to the sum of the rect- angles under AB and AO ... AC and CB are equal ( by Hypoth . ) , the rectangles AF and CH are equal ( by Prop . 36. B. 1 ) , but the rectangles CG and ...
... rectangle under the parts . OTHERWISE . The square of AB is equal to the sum of the rect- angles under AB and AO ... AC and CB are equal ( by Hypoth . ) , the rectangles AF and CH are equal ( by Prop . 36. B. 1 ) , but the rectangles CG and ...
Side 50
... under AD and DB is equal to the sum of the rectangles under AC and DB , and under CD and DB , ( by Prop . 1. B. 2 ) ; but the rectangle under AC and DB is equal to the rectangle under CB and DB ( because AC and CB are equal ) , or to the ...
... under AD and DB is equal to the sum of the rectangles under AC and DB , and under CD and DB , ( by Prop . 1. B. 2 ) ; but the rectangle under AC and DB is equal to the rectangle under CB and DB ( because AC and CB are equal ) , or to the ...
Side 51
... AC is the greater line , CD the less , and DB the 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 ...
... AC is the greater line , CD the less , and DB the 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 ...
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.