The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have ...
... magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have ...
Σελίδα 90
... four proportionals , and it is inferred that the second is to the first as the fourth to the third . Prop . B. Book ... magnitudes are taken , two and two . XIX . Ex aequali , from equality . This term is used simply by itself , when the ...
... four proportionals , and it is inferred that the second is to the first as the fourth to the third . Prop . B. Book ... magnitudes are taken , two and two . XIX . Ex aequali , from equality . This term is used simply by itself , when the ...
Σελίδα 93
... fourth d . If , therefore , the first , & c . Q. E. D. e bg c d PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the ...
... fourth d . If , therefore , the first , & c . Q. E. D. e bg c d PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the ...
Σελίδα 95
... magnitudes , & c . Q. E. D. h b d e f h k PROPOSITION A. - THEOREM . If the first of four magnitudes has to the second the same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also ...
... magnitudes , & c . Q. E. D. h b d e f h k PROPOSITION A. - THEOREM . If the first of four magnitudes has to the second the same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also ...
Σελίδα 96
... magnitude a be to b as c is to d , then also inversely b is to a as d to c . Take of b and d any equimultiples ... four magnitudes , & c . Q. E. D. PROPOSITION C. — THEOREM . If the first be the same multiple of the second , or the ...
... magnitude a be to b as c is to d , then also inversely b is to a as d to c . Take of b and d any equimultiples ... four magnitudes , & c . Q. E. D. PROPOSITION C. — THEOREM . If the first be the same multiple of the second , or the ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 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...
Σελίδα 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.