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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Seite 7
... greater of two given straight lines to cut off a part equal to the less . ( References - Prop . 1. 2 ; def . 15 ; post . 3 ; ax . 1. ) Let AB and C be the given straight lines , of which AB is greater than C. It is required to cut off ...
... greater of two given straight lines to cut off a part equal to the less . ( References - Prop . 1. 2 ; def . 15 ; post . 3 ; ax . 1. ) Let AB and C be the given straight lines , of which AB is greater than C. It is required to cut off ...
Seite 12
... greater than the other . Let AB be the greater ; and from it cut off DB equal to AC , the less , ( 1. 3. ) and join DC . DEMONSTRATION Then in the triangles DBC , ACB , because DB is assumed to be equal to AC , and BC is common to both ...
... greater than the other . Let AB be the greater ; and from it cut off DB equal to AC , the less , ( 1. 3. ) and join DC . DEMONSTRATION Then in the triangles DBC , ACB , because DB is assumed to be equal to AC , and BC is common to both ...
Seite 13
... greater than the angle BCD ; ( ax . 9 ) therefore the angle ADC must be greater also than BCD ; much more then must the angle BDC be greater than the angle BCD . Again , because in the triangle BCD , CB is assumed to be equal to BD ...
... greater than the angle BCD ; ( ax . 9 ) therefore the angle ADC must be greater also than BCD ; much more then must the angle BDC be greater than the angle BCD . Again , because in the triangle BCD , CB is assumed to be equal to BD ...
Seite 14
... greater than the angle BCD ; much more then must the angle BDC be greater than the angle BCD . Again , because in the triangle BCD , CB is assumed to be equal to ᎠᏴ , therefore the angle BDC must be equal to the angle BCD ; ( 1. 5 ) ...
... greater than the angle BCD ; much more then must the angle BDC be greater than the angle BCD . Again , because in the triangle BCD , CB is assumed to be equal to ᎠᏴ , therefore the angle BDC must be equal to the angle BCD ; ( 1. 5 ) ...
Seite 23
... greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE . In the same manner , if the side BC be bisected , and AC be produced to G , it may be demonstrated that the angle BCG , that is , the angle ACD , ( I ...
... greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE . In the same manner , if the side BC be bisected , and AC be produced to G , it may be demonstrated that the angle BCG , that is , the angle ACD , ( I ...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
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Seite 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...
Seite xiv - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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'.
Seite 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.
Seite 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...