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 14.
Σελίδα 99
... indices of the similar quantities , placing their sum over the common letter or letters ; and if the multiplier and multiplicand have like signs , place plus before the product , but if unlike , place minus before it . -y Secondly ...
... indices of the similar quantities , placing their sum over the common letter or letters ; and if the multiplier and multiplicand have like signs , place plus before the product , but if unlike , place minus before it . -y Secondly ...
Σελίδα 100
... indices becomes 1 , that is a1 . Wherefore multiplication of similar quantities is performed by adding their indices , and prefixing the sum to the right hand of the common letter or letters . Ex . 6 . Ex . 7 . Ex . 8 . Ex . 9 . a a2 aa ...
... indices becomes 1 , that is a1 . Wherefore multiplication of similar quantities is performed by adding their indices , and prefixing the sum to the right hand of the common letter or letters . Ex . 6 . Ex . 7 . Ex . 8 . Ex . 9 . a a2 aa ...
Σελίδα 101
... indices of similar quan- tities . In the 14th Example , the index of a ist , and the index of a is 1 , therefore , by adding these indices , we have 11 = , for the index of the product of a multiplied by a ; and then , multiplying ✓ by ...
... indices of similar quan- tities . In the 14th Example , the index of a ist , and the index of a is 1 , therefore , by adding these indices , we have 11 = , for the index of the product of a multiplied by a ; and then , multiplying ✓ by ...
Σελίδα 102
... indices of the other products may be similarly found . In these two Examples we have the proof of the 4th Proposition of the Second Book , a2 and b2 being the squares of the parts , and 2ab equal to twice the rectangle under the parts ...
... indices of the other products may be similarly found . In these two Examples we have the proof of the 4th Proposition of the Second Book , a2 and b2 being the squares of the parts , and 2ab equal to twice the rectangle under the parts ...
Σελίδα 104
... indices , and then the student can advance with ease to himself . By referring to the 12th Definition , ( given at the end of 1st Book ) you will see the proper- ties of the 1st Example in this Case ; but it may be further added , that ...
... indices , and then the student can advance with ease to himself . By referring to the 12th Definition , ( given at the end of 1st Book ) you will see the proper- ties of the 1st Example in this Case ; but it may be further added , that ...
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.