Euclid's Elements of Geometry |
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Page 3
... opposite sides are parallel . 31. A square is a quadrilateral figure , which is equi- lateral and equiangular . 32. Rectilineal figures which have more than four sides , are called polygons . POSTULATES . 1. Let it be granted that a ...
... opposite sides are parallel . 31. A square is a quadrilateral figure , which is equi- lateral and equiangular . 32. Rectilineal figures which have more than four sides , are called polygons . POSTULATES . 1. Let it be granted that a ...
Page 6
... ) ; the bases ( EF and AC ) will be equal ; and the angles at the bases , opposite to equal sides , will be equal ( E to A and F to C ) : and also the triangles themselves are equal . E FA C For if the triangles be so applied 6 FIRST BOOK .
... ) ; the bases ( EF and AC ) will be equal ; and the angles at the bases , opposite to equal sides , will be equal ( E to A and F to C ) : and also the triangles themselves are equal . E FA C For if the triangles be so applied 6 FIRST BOOK .
Page 8
... opposite . PROPOSITION VI . THEOREM . If two angles ( B and C ) of a triangle ( BAC ) be equal , the sides opposite to them ( AC and AB ) are equal . D If not , let one of them BA be made greater than the other , cut off a right line BD ...
... opposite . PROPOSITION VI . THEOREM . If two angles ( B and C ) of a triangle ( BAC ) be equal , the sides opposite to them ( AC and AB ) are equal . D If not , let one of them BA be made greater than the other , cut off a right line BD ...
Page 10
... opposite to the equal sides are equal , and also the triangles themselves . PROPOSITION IX . PROBLEM . To cut a given rectilineal angle ( BAC ) into two equal parts . From A take the equals AD and AE ( by Prop . 3 ) , draw DE , and upon ...
... opposite to the equal sides are equal , and also the triangles themselves . PROPOSITION IX . PROBLEM . To cut a given rectilineal angle ( BAC ) into two equal parts . From A take the equals AD and AE ( by Prop . 3 ) , draw DE , and upon ...
Page 11
... opposite to the equal sides DF and EF are equal ( by Schol . Prop . 8 ) ; and therefore FC is 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 ...
... opposite to the equal sides DF and EF are equal ( by Schol . Prop . 8 ) ; and therefore FC is 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 ...
Other editions - View all
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2018 |
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2022 |
Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington No preview available - 2015 |
Common terms and phrases
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
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 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.
Page 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.
Page 127 - In any proportion, the product of the means is equal to the product of the extremes.
Page 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.
Page 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.
Page 213 - ... are to one another in the duplicate ratio of their homologous sides.
Page 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.
Page 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.