The first six books of the Elements of Euclid, with numerous exercises |
Αναζήτηση στο βιβλίο
Σελίδα 89
Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . VII . When of the equimultiples ...
Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . VII . When of the equimultiples ...
Σελίδα 90
In proportionals , the antecedent terms are called homologous to one another , as also the consequents to one another . Geometers make use of the following technical words to signify certain ways of changing either the order or ...
In proportionals , the antecedent terms are called homologous to one another , as also the consequents to one another . Geometers make use of the following technical words to signify certain ways of changing either the order or ...
Σελίδα 95
... or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROPOSITION B. - THEOREM . If four magnitudes are proportionals BOOK V. PROPS . VI . , A. 95 35.
... or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROPOSITION B. - THEOREM . If four magnitudes are proportionals BOOK V. PROPS . VI . , A. 95 35.
Σελίδα 96
If four magnitudes are proportionals , they are proportionals also when taken g a h c inversely . IF 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 whatever e and f ...
If four magnitudes are proportionals , they are proportionals also when taken g a h c inversely . IF 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 whatever e and f ...
Σελίδα 101
If any number of magnitudes be proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . LET any number of magnitudes a , b , c , d , e , f be ...
If any number of magnitudes be proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . LET any number of magnitudes a , b , c , d , e , f be ...
Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
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.