The school Euclid: comprising the first four books, by A.K. Isbister |
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Αποτελέσματα 1 - 5 από τα 33.
Σελίδα 55
It is required to describe a square upon AB . c B CONSTRUCTION E From the point A draw AC at right angles to AB , ( 1. 11 ) and make AD equal to AB , ( I. 3 ) through the point D draw DE parallel to AB , ( 1.
It is required to describe a square upon AB . c B CONSTRUCTION E From the point A draw AC at right angles to AB , ( 1. 11 ) and make AD equal to AB , ( I. 3 ) through the point D draw DE parallel to AB , ( 1.
Σελίδα 56
30. ) Let ABC be a right - angled triangle , having the right angle BAC . Then the square described upon the side BC , shall be equal to the squares described upon BA , AC . F G H B D E CONSTRUCTION On BC describe the square BDEC , ( 1.
30. ) Let ABC be a right - angled triangle , having the right angle BAC . Then the square described upon the side BC , shall be equal to the squares described upon BA , AC . F G H B D E CONSTRUCTION On BC describe the square BDEC , ( 1.
Σελίδα 57
and the square BDEC is described upon the straight line BC , and the squares GB , HC , upon BA , AC ; wherefore the square upon the side BC , is equal to the squares upon the sides BA , AC . Therefore , in any right - angled triangle ...
and the square BDEC is described upon the straight line BC , and the squares GB , HC , upon BA , AC ; wherefore the square upon the side BC , is equal to the squares upon the sides BA , AC . Therefore , in any right - angled triangle ...
Σελίδα 58
B CONSTRUCTION From the point A draw AD at right angles to AC , ( 1. 11 ) and make AD equal to BA , ( 1. 3 ) and join DC . ... herefore the square of DC is equal to the squares of DA , AC ; ( 1. 47 ) and the square of BC is equal to the ...
B CONSTRUCTION From the point A draw AD at right angles to AC , ( 1. 11 ) and make AD equal to BA , ( 1. 3 ) and join DC . ... herefore the square of DC is equal to the squares of DA , AC ; ( 1. 47 ) and the square of BC is equal to the ...
Σελίδα 61
Let AB be divided into any two parts in C. Then the rectangle * contained by AB and BC , together with the rectangle contained by AB and AC , shall be equal to the square of AB . A C B D FE CONSTRUCTION Upon AB describe the square ADEB ...
Let AB be divided into any two parts in C. Then the rectangle * contained by AB and BC , together with the rectangle contained by AB and AC , shall be equal to the square of AB . A C B D FE CONSTRUCTION Upon AB describe the square ADEB ...
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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 |