The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 24
... parallelogram a cdb into two equal parts . Q. E. D. : PROPOSITION XXXV . - THEOREM . Parallelograms upon the same base , and between the same parallels , are equal to one another . LET the parallelograms a b c d , ebcf ( see the second ...
... parallelogram a cdb into two equal parts . Q. E. D. : PROPOSITION XXXV . - THEOREM . Parallelograms upon the same base , and between the same parallels , are equal to one another . LET the parallelograms a b c d , ebcf ( see the second ...
Página 25
... parallelogram a b c d is equal to the parallelogram e bcf . There- fore parallelograms upon the same base , & c . Q. E. D. PROPOSITION XXXVI . — THEOREM . Parallelograms upon equal bases , and between the same parallels , are equal to ...
... parallelogram a b c d is equal to the parallelogram e bcf . There- fore parallelograms upon the same base , & c . Q. E. D. PROPOSITION XXXVI . — THEOREM . Parallelograms upon equal bases , and between the same parallels , are equal to ...
Página 26
... parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it but the halves of equal things are equal ( 7 ax . ) ; therefore the ...
... parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it but the halves of equal things are equal ( 7 ax . ) ; therefore the ...
Página 27
... parallelogram and triangle be upon the same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram abcd and the triangle ebc be upon the same a d b e base bc , and between the ...
... parallelogram and triangle be upon the same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram abcd and the triangle ebc be upon the same a d b e base bc , and between the ...
Página 28
... parallelogram abcd is double ( i . 34 ) of the triangle abc , because the diameter ac divides it into two equal parts ; wherefore abcd is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION ...
... parallelogram abcd is double ( i . 34 ) of the triangle abc , because the diameter ac divides it into two equal parts ; wherefore abcd is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION ...
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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.