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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Αποτελέσματα 1 - 5 από τα 27.
Σελίδα 129
... ratio and proportion , as far as regards their utility in connexion with Equations . When two quantities are compared together , that is to say , ab or 10 : 5 , the first is called the ante- cedent , and the second the consequent , and ...
... ratio and proportion , as far as regards their utility in connexion with Equations . When two quantities are compared together , that is to say , ab or 10 : 5 , the first is called the ante- cedent , and the second the consequent , and ...
Σελίδα 163
... Ratio is a mutual relation of two magnitudes of the same kind , in respect of quantity . 4. Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the greater . 5. Magnitudes are said to be ...
... Ratio is a mutual relation of two magnitudes of the same kind , in respect of quantity . 4. Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the greater . 5. Magnitudes are said to be ...
Σελίδα 164
... ratio of that which it has to the second , namely , of the ratio of A to B. 11. When four magnitudes are proportional , one after the other ( A to B as B to C , and B to C as C to D ) , the first is said to have to the fourth ( A to D ) ...
... ratio of that which it has to the second , namely , of the ratio of A to B. 11. When four magnitudes are proportional , one after the other ( A to B as B to C , and B to C as C to D ) , the first is said to have to the fourth ( A to D ) ...
Σελίδα 165
... ratio , the first is to the last in the first series , as the first to the last in the next series .. Of this there are the two following species : — 20. Ex æquo ordinate ( from orderly equality ) , when the first magnitude will be to ...
... ratio , the first is to the last in the first series , as the first to the last in the next series .. Of this there are the two following species : — 20. Ex æquo ordinate ( from orderly equality ) , when the first magnitude will be to ...
Σελίδα 177
... ratio , are equal to one another . ratio to the And magni- ( C ) has the PART 1. - For , if possible , let one of them , A , be less than the other , B , and there can be taken a submultiple of it , which is oftener contained in C ...
... ratio , are equal to one another . ratio to the And magni- ( C ) has the PART 1. - For , if possible , let one of them , A , be less than the other , B , and there can be taken a submultiple of it , which is oftener contained in C ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 20 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 129 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 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.
Σελίδα 215 - ... are to one another in the duplicate ratio of their homologous sides.
Σελίδα 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.