Euclid's Elements of Geometry |
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Page vi
... Equation ; therefore , it is probable , that we had the word from the Arabic name of the Art , and not from the Philosopher Geber . It appears that the Arabians received it from the Persians and Indians ; but the Persians seem to refer ...
... Equation ; therefore , it is probable , that we had the word from the Arabic name of the Art , and not from the Philosopher Geber . It appears that the Arabians received it from the Persians and Indians ; but the Persians seem to refer ...
Page vii
... Equations of the First Degree 99 99 Second Degree • Numerical Proof of Euclid's Second Book Algebraic " 9 99 Fourth Book Fifth Book Sixth Book Trigonometry Appendix PAGE 1 5 39 40 42 44 61 65 97 103 111 · 120 123 · · 127 • 138 140 • 143 ...
... Equations of the First Degree 99 99 Second Degree • Numerical Proof of Euclid's Second Book Algebraic " 9 99 Fourth Book Fifth Book Sixth Book Trigonometry Appendix PAGE 1 5 39 40 42 44 61 65 97 103 111 · 120 123 · · 127 • 138 140 • 143 ...
Page 126
... 3a4 = remainder . a¤ + 6a5 + 15aa + 2a3 + 15a2 + 6a + 1 = 3rd power of the quotient . Any root out of any given quantity can be extracted by this Ruie . EQUATIONS . It will be requisite here to briefly state 126 THIRD BOOK .
... 3a4 = remainder . a¤ + 6a5 + 15aa + 2a3 + 15a2 + 6a + 1 = 3rd power of the quotient . Any root out of any given quantity can be extracted by this Ruie . EQUATIONS . It will be requisite here to briefly state 126 THIRD BOOK .
Page 127
... equation is the equality of two quantities . The assemblage of quantities at the same side of the sign is called the member or side ; an equation has two sides . That which is at the left is called the first side , and the other is ...
... equation is the equality of two quantities . The assemblage of quantities at the same side of the sign is called the member or side ; an equation has two sides . That which is at the left is called the first side , and the other is ...
Page 128
... equation 3x + 7 = 8x 12 , by chance , for to serve for example , it ought to be considered ( likewise all those of which we shall speak ) as coming from a problem of which we can always find an expression , by converting the equation ...
... equation 3x + 7 = 8x 12 , by chance , for to serve for example , it ought to be considered ( likewise all those of which we shall speak ) as coming from a problem of which we can always find an expression , by converting the equation ...
Other editions - View all
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2018 |
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2022 |
Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington No preview available - 2015 |
Common terms and phrases
absurd AC and CB AC by Prop AC is equal angle ABC angles by Prop arch base bisected centre circumference CKMB co-efficient Const contained in CD contained oftener divided divisor double draw drawn equal angles equal by Constr equal by Hypoth equal by Prop equal to twice equation equi equi-multiples equi-submultiples equiangular equilateral external angle fore four magnitudes proportional given angle given circle given line given right line given triangle gonal half a right inscribed less multiplying oftener contained parallel parallelogram perpendicular PROPOSITION quantities rectangle under AC rectilineal figure remaining angles remaining side right angles right line AC Schol segment side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 207 - ... 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.
Page 216 - 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.
Page 127 - In any proportion, the product of the means is equal to the product of the extremes.
Page 161 - 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.
Page 112 - 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.
Page 213 - ... are to one another in the duplicate ratio of their homologous sides.
Page 163 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Page 88 - 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.