Euclid's Elements of GeometryBell & Daldy, 1872 - 261 sider |
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Side 34
... difference between two given rectilineal figures , can be found , by applying parallelograms equal to both , to the same right line , and in the same angle , for the difference of these will be a parallelogram , equal to the given ...
... difference between two given rectilineal figures , can be found , by applying parallelograms equal to both , to the same right line , and in the same angle , for the difference of these will be a parallelogram , equal to the given ...
Side 36
... difference cf the squares of the given lines , according as the given sides be about the right angle , or not ; if about it , take the sum , if not , take the difference . COR . 2. - Given any number of squares , to find a square equal ...
... difference cf the squares of the given lines , according as the given sides be about the right angle , or not ; if about it , take the sum , if not , take the difference . COR . 2. - Given any number of squares , to find a square equal ...
Side 37
... difference of the squares of AB and BC , is equal to the difference between the sum of the of AD and DB , and the sum of the squares of CD and DB ( by Ax . 3 ) ; or taking away the common square of DB , is equal to the difference ...
... difference of the squares of AB and BC , is equal to the difference between the sum of the of AD and DB , and the sum of the squares of CD and DB ( by Ax . 3 ) ; or taking away the common square of DB , is equal to the difference ...
Side 40
... difference or that which remains in taking b from a ; in the same way a b + c , or a + c b , signifies that a and c ought to be joined together , and that 6 ought to be taken from the whole . - - 5. The sign x indicates multiplication ...
... difference or that which remains in taking b from a ; in the same way a b + c , or a + c b , signifies that a and c ought to be joined together , and that 6 ought to be taken from the whole . - - 5. The sign x indicates multiplication ...
Side 49
... differences of them and the halves are equal , namely , the segments AE and CF , EB and FD . A C D B COR . 3. - The rectangle under the sum and difference of two lines , is equal to the difference of the squares of these lines . Because ...
... differences of them and the halves are equal , namely , the segments AE and CF , EB and FD . A C D B COR . 3. - The rectangle under the sum and difference of two lines , is equal to the difference of the squares of these lines . Because ...
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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.