The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 99
... compounded of two equal ratios . — viz . , the ratio of the first to the second , and the ratio of the second to the third ; hence , it is called duplicate ratio . XI . When four magnitudes are continual proportionals , the first is ...
... compounded of two equal ratios . — viz . , the ratio of the first to the second , and the ratio of the second to the third ; hence , it is called duplicate ratio . XI . When four magnitudes are continual proportionals , the first is ...
Σελίδα 120
... compounded of equal ratios , are equal to one another . Let A be to B , as D is to E ; and B to C , as E is to F. The ratio compounded of the ratios of A to B , and of B to C , which ( Def . A ) is the ratio of A to C , is equal to the ...
... compounded of equal ratios , are equal to one another . Let A be to B , as D is to E ; and B to C , as E is to F. The ratio compounded of the ratios of A to B , and of B to C , which ( Def . A ) is the ratio of A to C , is equal to the ...
Σελίδα 121
... compounded of several other ratios ; and if one of the first ratios , or the ratio which is compounded of several of them , be equal to one of the last ratios , or to the ratio which is compounded of several of them ; the remaining ...
... compounded of several other ratios ; and if one of the first ratios , or the ratio which is compounded of several of them , be equal to one of the last ratios , or to the ratio which is compounded of several of them ; the remaining ...
Σελίδα 122
... compounded of the ratios of h to k , and k to 1 , which are equal to the remaining first ratios , viz . , of C to D , and E to F. Also , let the ratio of m top , be that which is compounded of the ratios of m to n , n to o , and o to p ...
... compounded of the ratios of h to k , and k to 1 , which are equal to the remaining first ratios , viz . , of C to D , and E to F. Also , let the ratio of m top , be that which is compounded of the ratios of m to n , n to o , and o to p ...
Σελίδα 143
... compounded of the ratios of K to L , and L to M ( V. Def . A ) . Therefore K has to M the ratio compounded of the ratios of the sides . Because BC is to CG , as the parallelogram A C is to the parallelogram CH ( VI . 1 ) . But BC is to ...
... compounded of the ratios of K to L , and L to M ( V. Def . A ) . Therefore K has to M the ratio compounded of the ratios of the sides . Because BC is to CG , as the parallelogram A C is to the parallelogram CH ( VI . 1 ) . But BC is to ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Πλήρης προβολή - 1881 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C ABC is equal ABCD altitude angle ABC angle BAC base bisected Book centre circle circle ABC circumference common compounded cone Const contained Corollary cylinder definition demonstration described diameter divided double draw drawn equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half homologous inscribed join less magnitudes manner meet multiple opposite parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proposition proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar similarly solid solid angle sphere square Take taken THEOREM third touch triangle ABC vertex Wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 42 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 130 - 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.
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 3 - 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.
Σελίδα 143 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Σελίδα 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Σελίδα 115 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Σελίδα 45 - 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...