Euclid's Elements of GeometryBell & Daldy, 1872 - 261 sider |
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Side 98
... example . But in Ex . 3 , the signs are not similar , therefore they make minus . Exs . 4 and 5 are both the same ... Examples 6 , 7 , and 8 , is found by the second part of the general Rule ; and the product of the 9th is found by both ...
... example . But in Ex . 3 , the signs are not similar , therefore they make minus . Exs . 4 and 5 are both the same ... Examples 6 , 7 , and 8 , is found by the second part of the general Rule ; and the product of the 9th is found by both ...
Side 99
... Examples require but little explanation , as all relative to them will appear evident , by strict attention to the adding of the indices of similar quan- tities . In the 14th Example , the index of a is , and the index of a is 1 ...
... Examples require but little explanation , as all relative to them will appear evident , by strict attention to the adding of the indices of similar quan- tities . In the 14th Example , the index of a is , and the index of a is 1 ...
Side 100
Euclid T. W. Herbert. By adding the indices in the 15th example , it is evident we have 2n for the index of a . In ... Examples we have the proof of the 4th Proposition of the Second Book , a2 and 62 being the squares of the parts , and ...
Euclid T. W. Herbert. By adding the indices in the 15th example , it is evident we have 2n for the index of a . In ... Examples we have the proof of the 4th Proposition of the Second Book , a2 and 62 being the squares of the parts , and ...
Side 101
... Answer .... b2a3 c2a3 + b4a2 + 3ab . - CASE 2 . - c4a2 + 3ac EXAMPLES WITH ANSWERS . -2s 1. - Multiply a " b " by a " + b2 " - + -23 + b Ans ... a · 2y + a1b - ≈ + a −1b − - 2. - Multiply a3b + a1 + a2b2 = THIRD BOOK . 101.
... Answer .... b2a3 c2a3 + b4a2 + 3ab . - CASE 2 . - c4a2 + 3ac EXAMPLES WITH ANSWERS . -2s 1. - Multiply a " b " by a " + b2 " - + -23 + b Ans ... a · 2y + a1b - ≈ + a −1b − - 2. - Multiply a3b + a1 + a2b2 = THIRD BOOK . 101.
Side 102
... Example in this Case : but it may be further added , that à indicates the nought power of la divided by a thus , y - y a Again , = 1 ; and a - indicates a therefore since y subtracted from ay αν y leaves the nought power of a , it is ...
... Example in this Case : but it may be further added , that à indicates the nought power of la divided by a thus , y - y a Again , = 1 ; and a - indicates a therefore since y subtracted from ay αν y leaves the nought power of a , it is ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 18 - If two triangles have two sides of the one equal to two sides of the...
Side 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 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.
Side 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.
Side 127 - In any proportion, the product of the means is equal to the product of the extremes.
Side 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.
Side 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.
Side 213 - ... are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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.