The school Euclid: comprising the first four books, by A.K. Isbister |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 22
If one side of a triangle be produced , then the exterior angle is greater than either of the interior opposite angles . ( References - Prop . 1. 3 , 4 , 10 , 15 ; ax . 9. ) Let ABC be a triangle , and let the side 22 [ BOOK I. THE ...
If one side of a triangle be produced , then the exterior angle is greater than either of the interior opposite angles . ( References - Prop . 1. 3 , 4 , 10 , 15 ; ax . 9. ) Let ABC be a triangle , and let the side 22 [ BOOK I. THE ...
Σελίδα 23
Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater than either of the angles ABC or CAB . A A B CONSTRUCTION Bisect AC in E , ( 1. 10 ) and join BE , produce BE to F , and make EF ...
Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater than either of the angles ABC or CAB . A A B CONSTRUCTION Bisect AC in E , ( 1. 10 ) and join BE , produce BE to F , and make EF ...
Σελίδα 24
Then any two of its angles shall be together greater than two right angles . B CONSTRUCTION Produce the side BC to D. DEMONSTRATION Because ACD is the exterior angle of the triangle ABC , therefore the angle ACD is greater than the ...
Then any two of its angles shall be together greater than two right angles . B CONSTRUCTION Produce the side BC to D. DEMONSTRATION Because ACD is the exterior angle of the triangle ABC , therefore the angle ACD is greater than the ...
Σελίδα 25
Then the angle ABC shall be greater than the angle ВСА . D B CONSTRUCTION Because the side AC is greater than the side AB , make AD equal to AB , ( 1. 3. ) and join BD . DEMONSTRATION Because the angle ADB is the exterior angle of the ...
Then the angle ABC shall be greater than the angle ВСА . D B CONSTRUCTION Because the side AC is greater than the side AB , make AD equal to AB , ( 1. 3. ) and join BD . DEMONSTRATION Because the angle ADB is the exterior angle of the ...
Σελίδα 28
Again , because the exterior angle of a triangle is greater than the interior and opposite angle ; ( 1. 16 ) therefore the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the ...
Again , because the exterior angle of a triangle is greater than the interior and opposite angle ; ( 1. 16 ) therefore the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of 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 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 side BC 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 |