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 153
... proportionals . 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 of four magnitudes ( taken as in the fifth definition ) ...
... proportionals . 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 of four magnitudes ( taken as in the fifth definition ) ...
Σελίδα 154
... proportionals , so that they continue still to be proportionals . XIII . This Permutanao , or alternando , by permutation or alternately . word is used when there are four proportionals , and it is inferred that the first has the same ...
... proportionals , so that they continue still to be proportionals . XIII . This Permutanao , or alternando , by permutation or alternately . word is used when there are four proportionals , and it is inferred that the first has the same ...
Σελίδα 155
... proportionals , and it is inferred , that the excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . -Prop . xvII . Book v . XVII . Convertendo , by conversion ; when ...
... proportionals , and it is inferred , that the excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . -Prop . xvII . Book v . XVII . Convertendo , by conversion ; when ...
Σελίδα 164
... proportionals , they are proportionals also when taken inversely . ( Reference - v . def . 5. ) Let A be to B , as C is to D. Then also inversely , B shall be to A , as D to C. A B C D G E H F CONSTRUCTION Take of B and D any ...
... proportionals , they are proportionals also when taken inversely . ( Reference - v . def . 5. ) Let A be to B , as C is to D. Then also inversely , B shall be to A , as D to C. A B C D G E H F CONSTRUCTION Take of B and D any ...
Σελίδα 173
... proportionals ; then as one of the antecedents is to its consequent , so shall all the ante- cedents taken together be to all the consequents . ( References - Prop . v . 1 , def . 5. ) Let any number of magnitudes A , B , C , D , E , F ...
... proportionals ; then as one of the antecedents is to its consequent , so shall all the ante- cedents taken together be to all the consequents . ( References - Prop . v . 1 , def . 5. ) Let any number of magnitudes A , B , C , D , E , F ...
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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...