Euclid's Elements of GeometryBell & Daldy, 1872 - 261 sider |
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Resultat 1-5 av 52
Side 11
... perpendicular to the given right line AB ( by Def . 11. ) SCHOL . - By the same method a perpendicular can be erected at the extremities of a given right line , if the right line be first produced . PROPOSITION XII . PROBLEM . From a ...
... perpendicular to the given right line AB ( by Def . 11. ) SCHOL . - By the same method a perpendicular can be erected at the extremities of a given right line , if the right line be first produced . PROPOSITION XII . PROBLEM . From a ...
Side 12
... perpendicular to the given line . For draw CE and CF ; and in the triangles EDC and FDC , the sides EC , FC will be equal ( by Def . 15 ) , but ED , FD are also equal ( by Constr . ) and CD com- mon ; therefore the angles EDC and FDC ...
... perpendicular to the given line . For draw CE and CF ; and in the triangles EDC and FDC , the sides EC , FC will be equal ( by Def . 15 ) , but ED , FD are also equal ( by Constr . ) and CD com- mon ; therefore the angles EDC and FDC ...
Side 14
... perpendicular falls at the side of the acute angle . For , if it be possible , let BA , perpendicular to the right line ED , fall at the side of the obtuse angle BCE , and the angle BAE will be less than the angle BCE ( by Def . 12 ) ...
... perpendicular falls at the side of the acute angle . For , if it be possible , let BA , perpendicular to the right line ED , fall at the side of the obtuse angle BCE , and the angle BAE will be less than the angle BCE ( by Def . 12 ) ...
Side 16
... perpendicular , and the other not , BC will be less than BA . E A C B For in the triangle ABC , since the angle BCA is right , BAC will be acute ( by Cor . Prop . 17 ) , therefore BC is opposite the less angle , and therefore is less ...
... perpendicular , and the other not , BC will be less than BA . E A C B For in the triangle ABC , since the angle BCA is right , BAC will be acute ( by Cor . Prop . 17 ) , therefore BC is opposite the less angle , and therefore is less ...
Side 36
... an interval , describe a semicircle AEF ; through D draw DE perpendicular to AD , it will be the right line sought for . For draw BE . The square of BE , or of BA , it being equal to BE , is equal to the squares 36 FIRST BOOK .
... an interval , describe a semicircle AEF ; through D draw DE perpendicular to AD , it will be the right line sought for . For draw BE . The square of BE , or of BA , it being equal to BE , is equal to the squares 36 FIRST BOOK .
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Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington Ingen forhåndsvisning tilgjengelig - 2015 |
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.