Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
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Σελίδα 108
Ratio is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . IV . Magnitudes are said to be of the same kind , when the less can be multiplied so as to exceed the greater ; and it is only ...
Ratio is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . IV . Magnitudes are said to be of the same kind , when the less can be multiplied so as to exceed the greater ; and it is only ...
Σελίδα 109
When there is any number of magnitudes greater than two , of which the first has to the second the same ratio that the second has to the third , and the second to the third the same ratio wbich the third has to the fourth , and so on ...
When there is any number of magnitudes greater than two , of which the first has to the second the same ratio that the second has to the third , and the second to the third the same ratio wbich the third has to the fourth , and so on ...
Σελίδα 110
to C , a ratio , which is compounded of two equal ratios , is dupli" cate of either of these ratios . " XII . If four magnitudes are continual proportionals , the ratio of the first to the fourth is said to be triplicate of the ratio of ...
to C , a ratio , which is compounded of two equal ratios , is dupli" cate of either of these ratios . " XII . If four magnitudes are continual proportionals , the ratio of the first to the fourth is said to be triplicate of the ratio of ...
Σελίδα 113
If the first of four magnitudes has the same ratio to the second which the third has to the fourth , and if any equimultiples whatever be taken of the first and third , and any whatever , of the second and fourth ; the anultiple of the ...
If the first of four magnitudes has the same ratio to the second which the third has to the fourth , and if any equimultiples whatever be taken of the first and third , and any whatever , of the second and fourth ; the anultiple of the ...
Σελίδα 115
Equal magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes . Let A and B be equal magnitudes , and C any other ; A : C :: B : C . Let mA , mB , be any equimultiples of A ...
Equal magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes . Let A and B be equal magnitudes , and C any other ; A : C :: B : C . Let mA , mB , be any equimultiples of A ...
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ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
| Συγγραφέας | John Playfair |
| Εκδότης | E. Duyckinck, and George Long, 1824 |
| Πρωτότυπο από | Πανεπιστήμιο της Ιντιάνα |
| Ψηφιοποιήθηκε στις | 15 Ιαν. 2009 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |