Euclid's Elements of GeometryBell & Daldy, 1872 - 261 sider |
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Resultat 1-5 av 33
Side v
... constructed on the parts of any divided line , & c . The Third Book treats of the properties of the circle . The Fourth Book treats of such regular figures as can be described by a circle ; and also of the division of the circum ...
... constructed on the parts of any divided line , & c . The Third Book treats of the properties of the circle . The Fourth Book treats of such regular figures as can be described by a circle ; and also of the division of the circum ...
Side 5
... constructed upon the given right line AB ; but it is equilateral ; for AC is equal to AB , because they are the ... construct an equilateral triangle ADB ( by Prop . 1 ) . From the centre B , with the interval BC , describe a circle ...
... constructed upon the given right line AB ; but it is equilateral ; for AC is equal to AB , because they are the ... construct an equilateral triangle ADB ( by Prop . 1 ) . From the centre B , with the interval BC , describe a circle ...
Side 6
... constructed . PROPOSITION III . PROBLEM . From the greater of two given right lines ( AB and CF ) to cut off a part equal to the less . From either extremity A of the greater right line , draw AD , equal o the less CF of the given lines ...
... constructed . PROPOSITION III . PROBLEM . From the greater of two given right lines ( AB and CF ) to cut off a part equal to the less . From either extremity A of the greater right line , draw AD , equal o the less CF of the given lines ...
Side 9
... constructed on the same right line cannot have their conterminous sides equal , if the vertex of each fall without the other . CEE Now let the vertex D of either fall within the other ; and draw CD ; produce AC and AD to E and F. Since ...
... constructed on the same right line cannot have their conterminous sides equal , if the vertex of each fall without the other . CEE Now let the vertex D of either fall within the other ; and draw CD ; produce AC and AD to E and F. Since ...
Side 11
... construct an equilateral triangle ACB ( by Prop . 1 ) ; bisect the angle ACB by the right line CD ( by Prop . 9 ) ; this will bisect the given right line in the point D. A D For in the triangles ACD , BCD , the sides AC and CB are equal ...
... construct an equilateral triangle ACB ( by Prop . 1 ) ; bisect the angle ACB by the right line CD ( by Prop . 9 ) ; this will bisect the given right line in the point D. A D For in the triangles ACD , BCD , the sides AC and CB are equal ...
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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.