The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 15
... reason , the exterior angle ceb of the triangle abe is greater than bac ; and it has been demonstrated that the angle bdc is greater than the angle ceb ; much greater then is the angle bdc than the angle bac . Therefore , if from the ...
... reason , the exterior angle ceb of the triangle abe is greater than bac ; and it has been demonstrated that the angle bdc is greater than the angle ceb ; much greater then is the angle bdc than the angle bac . Therefore , if from the ...
Σελίδα 24
... debcf , be not terminated in the same point d ; then , because abcd is a paral- lelogram , ad is equal ( i . 34 ) to bc ; for the same reason ef is equal to bc ; wherefore ad is equal ( 1 ax . 24 THE ELEMENTS OF EUCLID .
... debcf , be not terminated in the same point d ; then , because abcd is a paral- lelogram , ad is equal ( i . 34 ) to bc ; for the same reason ef is equal to bc ; wherefore ad is equal ( 1 ax . 24 THE ELEMENTS OF EUCLID .
Σελίδα 25
... reason , the parallelogram efgh is equal to the same ebch . Therefore also the parallelogram abcd is equal to efgh Wherefore parallelo- grams , & c . Q. E. D. PROPOSITION XXXVII . - THEOREM . Triangles upon the same base , and between ...
... reason , the parallelogram efgh is equal to the same ebch . Therefore also the parallelogram abcd is equal to efgh Wherefore parallelo- grams , & c . Q. E. D. PROPOSITION XXXVII . - THEOREM . Triangles upon the same base , and between ...
Σελίδα 29
... reason , the triangle kgc is equal to the triangle kfc . Then , because the triangle aek is equal to the triangle ahk , and the triangle kgc to kfc ; the triangle aek , together with the triangle kgc is equal to the triangle ahk ...
... reason , the triangle kgc is equal to the triangle kfc . Then , because the triangle aek is equal to the triangle ahk , and the triangle kgc to kfc ; the triangle aek , together with the triangle kgc is equal to the triangle ahk ...
Σελίδα 31
... reason , a b and ah are in the same straight line ; and because the angle dbc is equal to the angle fba , each of them being a right angle , add to each the angle abc , and the whole angle dba is equal ( 2 ax . ) to the whole fbc ; and ...
... reason , a b and ah are in the same straight line ; and because the angle dbc is equal to the angle fba , each of them being a right angle , add to each the angle abc , and the whole angle dba is equal ( 2 ax . ) to the whole fbc ; and ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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 perpendicular Q. E. D. PROPOSITION rectangle a b 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
Δημοφιλή αποσπάσματα
Σελίδα 40 - 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.
Σελίδα 2 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 19 - 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.
Σελίδα 27 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 36 - 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...
Σελίδα 13 - 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...
Σελίδα 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 2 - 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...
Σελίδα 124 - 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.