Elements of Euclid Adapted to Modern Methods in GeometryWilliam Collins, Sons,, 1874 - 216 σελίδες |
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Σελίδα 155
... proportional between , and the third a third proportional to , the other two . Schol . Thus a proportion must consist of three terms at least . 10. When the consequent of one ratio is the antecedent of another , and also the antecedent ...
... proportional between , and the third a third proportional to , the other two . Schol . Thus a proportion must consist of three terms at least . 10. When the consequent of one ratio is the antecedent of another , and also the antecedent ...
Σελίδα 158
... proportional . ( See Note , p . 161 , and schol . , p . 162 ) . The test in the definition applicable to such magnitudes , is that the equi - multiples of the first and third are greater together and less together than the corre ...
... proportional . ( See Note , p . 161 , and schol . , p . 162 ) . The test in the definition applicable to such magnitudes , is that the equi - multiples of the first and third are greater together and less together than the corre ...
Σελίδα 160
... proportional by the FIFTH DEFINITION , are proportional also by the arithmetical definition ; and conversely . This Definition may be thus stated : " Two ratios are equal , or four magnitudes proportional , when the first mag . nitude ...
... proportional by the FIFTH DEFINITION , are proportional also by the arithmetical definition ; and conversely . This Definition may be thus stated : " Two ratios are equal , or four magnitudes proportional , when the first mag . nitude ...
Σελίδα 166
... proportional magnitudes of the same kind , so that then we shall have , For since ' A is to B as C is to D , as A is to C so is B to D. A is to B as C is to D , A B Multiplying these equals by B , we have A = CxB D - and dividing these ...
... proportional magnitudes of the same kind , so that then we shall have , For since ' A is to B as C is to D , as A is to C so is B to D. A is to B as C is to D , A B Multiplying these equals by B , we have A = CxB D - and dividing these ...
Σελίδα 178
... proportional , and if the first of them be the greatest , the fourth shall be the least ; but if the first of them be the least , the fourth shall be the greatest . 9. If four magnitudes are proportionals , any multiple of the first ...
... proportional , and if the first of them be the greatest , the fourth shall be the least ; but if the first of them be the least , the fourth shall be the greatest . 9. If four magnitudes are proportionals , any multiple of the first ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Euclid Adapted to Modern Methods in Geometry Euclid,James Bryce,David Munn (F.R.S.E.) Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1874 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AC and CB altitude angle AOB BA and AC bisecting the angle centre chord circles touch circumference cloth coincide Const conv Cor.-Hence diagonal diameter divided draw equal angles equal to BC equal to twice equiangular equilateral triangle Euclid exterior angle Fcap GEOGRAPHY geometrical given circle given line given point given straight line greater half the perimeter Hence hypotenuse inscribed intersecting isosceles triangle less Let ABC LL.D meet middle point multiple opposite sides parallel to BC parallelogram perpendicular polygon produced Proposition Q. E. D. Cor Q. E. D. PROP radius ratio rectangle contained rectilineal figure reflex angle remaining angles required to prove right angles right-angled triangle schol segments shew shewn side BC square on AC tangent THEOREM triangle ABC twice the rectangle twice the square whole line
Δημοφιλή αποσπάσματα
Σελίδα 68 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 77 - 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 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.
Σελίδα 87 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.
Σελίδα 30 - Any two sides of a triangle are together greater than the third side.
Σελίδα 204 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...
Σελίδα 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 98 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.