The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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... Propositions Exercises III . Definitions 1 4 33 35 35 46 47 Propositions 48 Exercises IV . Definitions Propositions Exercises V. Definitions . Propositions Exercises VI . Definitions Propositions Exercises 73 75 76 87 89 91 115 116 ...
... Propositions Exercises III . Definitions 1 4 33 35 35 46 47 Propositions 48 Exercises IV . Definitions Propositions Exercises V. Definitions . Propositions Exercises VI . Definitions Propositions Exercises 73 75 76 87 89 91 115 116 ...
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... PROPOSITION I. - PROBLEM . To describe an equilateral triangle upon a given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . a From the centre a , at the distance ab ...
... PROPOSITION I. - PROBLEM . To describe an equilateral triangle upon a given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . a From the centre a , at the distance ab ...
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... PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw from the point a a straight line equal to bc ...
... PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw from the point a a straight line equal to bc ...
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... PROPOSITION IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases ...
... PROPOSITION IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases ...
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... PROPOSITION VI . - THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET abc be a triangle having the angle abc equal ...
... PROPOSITION VI . - THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET abc be a triangle having the angle abc equal ...
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Términos y frases comunes
a b c 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 pentagon perpendicular Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc 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.