The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 13
Euclides. are equal to the angles aed , deb . Take away the common angle a e d , and the remaining angle ce a is ... exterior angle of the triangle abc , acd is greater ( i . 16 ) than the interior and opposite angle abc ; to each of ...
Euclides. are equal to the angles aed , deb . Take away the common angle a e d , and the remaining angle ce a is ... exterior angle of the triangle abc , acd is greater ( i . 16 ) than the interior and opposite angle abc ; to each of ...
Página 14
... exterior angle of the triangle bd c , it is greater ( i . 16 ) than the interior and opposite angle dcb ; but a db ... angle bcd is greater than the angle acd ; therefore the angle op- d a bcd is greater than the angle adc THE ELEMENTS ...
... exterior angle of the triangle bd c , it is greater ( i . 16 ) than the interior and opposite angle dcb ; but a db ... angle bcd is greater than the angle acd ; therefore the angle op- d a bcd is greater than the angle adc THE ELEMENTS ...
Página 15
... angle bed of the triangle dcb is greater than its angle bdc , and that the greater ( i . 19 ) side is posite to the ... exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of the triangle ...
... angle bed of the triangle dcb is greater than its angle bdc , and that the greater ( i . 19 ) side is posite to the ... exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of the triangle ...
Página 19
... exterior angle bha of the triangle a hc is equal to its interior and opposite angle bca ; which is impossible ( i ... angle e df . Therefore , if two triangles , & c . Q. E. D. PROPOSITION XXVII . THEOREM . If a straight line falling ...
... exterior angle bha of the triangle a hc is equal to its interior and opposite angle bca ; which is impossible ( i ... angle e df . Therefore , if two triangles , & c . Q. E. D. PROPOSITION XXVII . THEOREM . If a straight line falling ...
Página 20
... exterior angle aefis greater ( i . 16 ) than the interior and opposite angle efg ; but it is also a f e b g d equal to it , which is impossible ; therefore a b and c d being produced do not meet towards b , d . In like manner it may be ...
... exterior angle aefis greater ( i . 16 ) than the interior and opposite angle efg ; but it is also a f e b g d equal to it , which is impossible ; therefore a b and c d being produced do not meet towards b , d . In like manner it may be ...
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Términos y frases comunes
abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc straight line drawn tiple touches the circle triangle abc triangle def twice the rectangle
Pasajes populares
Página 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Página 42 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 38 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Página 15 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Página 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 126 - 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.