The school Euclid: comprising the first four books, by A.K. Isbister |
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Αποτελέσματα 11 - 15 από τα 25.
Σελίδα 71
therefore the squares of AC , CE , are double of the squares of AC ; but because ACE is a right angle the square of EA is equal to the squares of AC , CE , ( 1. 47 ) therefore the square of EA is double of the square of AC .
therefore the squares of AC , CE , are double of the squares of AC ; but because ACE is a right angle the square of EA is equal to the squares of AC , CE , ( 1. 47 ) therefore the square of EA is double of the square of AC .
Σελίδα 73
And because EC is equal to CA , the square of EC is equal to the square of CA ; therefore the squares of EC , CA , are double of the square of CA ; but the square of EA is equal to the squares of EC , CA ; ( 1. 47 ) therefore the square ...
And because EC is equal to CA , the square of EC is equal to the square of CA ; therefore the squares of EC , CA , are double of the square of CA ; but the square of EA is equal to the squares of EC , CA ; ( 1. 47 ) therefore the square ...
Σελίδα 77
3 ) and the doubles of these are equal ; that is , twice the rectangle DB , BC , is equal to twice the rectangle BC , CD , and twice the square of BC ; therefore the squares of AB , BC , are equal to the square of AC , and twice the ...
3 ) and the doubles of these are equal ; that is , twice the rectangle DB , BC , is equal to twice the rectangle BC , CD , and twice the square of BC ; therefore the squares of AB , BC , are equal to the square of AC , and twice the ...
Σελίδα 97
... which does not pass through the centre , at right angles , it also bisects it ; ( III , 3 ) therefore AF is equal to FB , and AB double of AF ; for the same reason CD is double of CG ; but AB is equal to CD ; ( hyp . ) ...
... which does not pass through the centre , at right angles , it also bisects it ; ( III , 3 ) therefore AF is equal to FB , and AB double of AF ; for the same reason CD is double of CG ; but AB is equal to CD ; ( hyp . ) ...
Σελίδα 98
The same construction being made , it may be demonstrated as before , that AB is double of AF , and CD double of CG , and that the squares of EF , FA , are equal to the squares of EG , GC ; of which the square of FE is equal to the ...
The same construction being made , it may be demonstrated as before , that AB is double of AF , and CD double of CG , and that the squares of EF , FA , are equal to the squares of EG , GC ; of which the square of FE is equal to the ...
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The School Euclid: Comprising the First Four Books, by A.K. Isbister Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
The School Euclid: Comprising the First Four Books, by A.K. Isbister Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisect centre circle ABC circumference coincide common constr CONSTRUCTION DEMONSTRATION describe diameter distance divided double draw Edition equal equal to AC equilateral and equiangular exterior angle extremity fall figure four given circle given straight line greater half impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular produced proved Q. E. D. PROP reason rectangle contained References-Prop remaining angle right angles segment semicircle shown sides square of AC straight line AC THEOREM third touches the circle triangle ABC twice the rectangle wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 141 - 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 35 - 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 71 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
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 61 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Σελίδα 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 27 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Σελίδα 77 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.
Σελίδα 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The school Euclid: comprising the first four books, by A.K. Isbister |
| Συγγραφέας | Euclides |
| Επιμελητής | Alexander Kennedy Isbister |
| Εκδόθηκε | 1862 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 18 Απρ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |