The College Euclid: Comprising the First Six and the Parts of the Eleventh and Twelfth Books Read at the Universities ... By A. K. Isbister1865 |
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Σελίδα 152
... equimultiples what- soever of the first and third being taken , and any equimultiples what- soever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than ...
... equimultiples what- soever of the first and third being taken , and any equimultiples what- soever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than ...
Σελίδα 153
... equimultiples of four magnitudes ( taken as in the fifth definition ) , the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then , the first is ...
... equimultiples of four magnitudes ( taken as in the fifth definition ) , the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then , the first is ...
Σελίδα 155
... cross order ; and the inference is as in the 18th Definition . - Prop . XXIII . Book v . * Prop . 4. Lib . II Archimedis de sphæra et cylindro . AXIOMS . I. Equimultiples of the same , or of BOOK V. DEFINITIONS . 155.
... cross order ; and the inference is as in the 18th Definition . - Prop . XXIII . Book v . * Prop . 4. Lib . II Archimedis de sphæra et cylindro . AXIOMS . I. Equimultiples of the same , or of BOOK V. DEFINITIONS . 155.
Σελίδα 156
... equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple ... equimultiples of as many others , each of each ; then what multiple soever any one of them is of its part , the same ...
... equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple ... equimultiples of as many others , each of each ; then what multiple soever any one of them is of its part , the same ...
Σελίδα 157
... equimultiples of as many , each of each ; whatsoever multiple any one of them is of its part , the same multiple shall all the first magnitudes be of all the other For the same demonstration holds in any number of mag- nitudes , which ...
... equimultiples of as many , each of each ; whatsoever multiple any one of them is of its part , the same multiple shall all the first magnitudes be of all the other For the same demonstration holds in any number of mag- nitudes , which ...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal base BC bisect Book centre circle ABC circumference compounded constr DEMONSTRATION diameter double draw Edition English equal angles equal straight lines equal to BC equiangular equilateral and equiangular equimultiples Euclid exterior angle four magnitudes fourth French given circle given point given rectilineal angle given straight line gnomon Grammar greater ratio inscribed isosceles triangle join less Let ABC multiple opposite angles parallel parallelogram pentagon perpendicular plane polygon proportionals proposition Q. E. D. PROP rectangle contained rectilineal figure References-Prop remaining angle right angles segment similar solid angle square of AC straight line AC THEOREM third three straight lines touches the circle triangle ABC twice the rectangle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 140 - 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. either the sides adjacent to the equal...
Σελίδα xiv - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 310 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 33 - 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 vi - If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that part.
Σελίδα 310 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα xxxvii - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 69 - 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 of the other part.
Σελίδα 287 - If any point be taken in the diameter of a circle which is not the centre, of all the straight lines which can be drawn from it to the circumference, the greatest is that in which the centre is, and the other part of that diameter is the least...