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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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 10
... join FC , GB . DEMONSTRATION Because AF is equal to AG ; ( constr . ) and AB to AC ; ( hypoth . ) the two sides FA , AC , are equal to the two GA , AB , each to each , and they contain the angle FAG common to the two triangles AFC , AGB ...
... join FC , GB . DEMONSTRATION Because AF is equal to AG ; ( constr . ) and AB to AC ; ( hypoth . ) the two sides FA , AC , are equal to the two GA , AB , each to each , and they contain the angle FAG common to the two triangles AFC , AGB ...
Σελίδα 12
... join DC . DEMONSTRATION Then in the triangles DBC , ACB , because DB is assumed to be equal to AC , and BC is common to both , the two sides DB , BC , must be equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
... join DC . DEMONSTRATION Then in the triangles DBC , ACB , because DB is assumed to be equal to AC , and BC is common to both , the two sides DB , BC , must be equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
Σελίδα 13
... Join the vertices C and D by the straight line CD . DEMONSTRATION Because , in the triangle ACD , AC is assumed to be equal to AD , therefore the angle ACD must be equal to the angle ADC ; ( 1. 5 ) but the angle ACD is greater than the ...
... Join the vertices C and D by the straight line CD . DEMONSTRATION Because , in the triangle ACD , AC is assumed to be equal to AD , therefore the angle ACD must be equal to the angle ADC ; ( 1. 5 ) but the angle ACD is greater than the ...
Σελίδα 15
... given rectilineal angle . It is required to bisect it . A B F E CONSTRUCTION Take any point D in AB , from AC cut off AE equal to AD , ( 1. 3 ) and join DE ; upon the side of it opposite to A , describe BOOK I. PROP . IX . 15.
... given rectilineal angle . It is required to bisect it . A B F E CONSTRUCTION Take any point D in AB , from AC cut off AE equal to AD , ( 1. 3 ) and join DE ; upon the side of it opposite to A , describe BOOK I. PROP . IX . 15.
Σελίδα 16
... join AF . Then the straight line AF bisects the angle BAC . DEMONSTRATION Because AD is equal to AE , ( constr . ) and AF is common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to ...
... join AF . Then the straight line AF bisects the angle BAC . DEMONSTRATION Because AD is equal to AE , ( constr . ) and AF is common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to ...
Άλλες εκδόσεις - Προβολή όλων
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...