Euclid's Elements of geometry, books i. ii. iii. iv1862 |
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Αποτελέσματα 1 - 5 από τα 43.
Σελίδα 5
... straight lines CA , CB , to the points A and B. ( post . 1. ) D Then ABC shall be an equilateral triangle . B E Proof . - 1 . Because the point A is the centre of the circle BCD , AC is equal to AB . ( def . 15. ) 2. Because the point B ...
... straight lines CA , CB , to the points A and B. ( post . 1. ) D Then ABC shall be an equilateral triangle . B E Proof . - 1 . Because the point A is the centre of the circle BCD , AC is equal to AB . ( def . 15. ) 2. Because the point B ...
Σελίδα 6
... AL and BC are each of them equal to BG . 7. But things which are equal to the same thing are equal to one another , therefore AL is equal to BC . ( ax . 1. ) Conclusion . Therefore from the given point A a straight line AL has been ...
... AL and BC are each of them equal to BG . 7. But things which are equal to the same thing are equal to one another , therefore AL is equal to BC . ( ax . 1. ) Conclusion . Therefore from the given point A a straight line AL has been ...
Σελίδα 7
... AC , equal to the two sides DE , DF , each to each , viz . AB equal to DE , and AC equal to DF . 2. And the angle ... straight line AB on the straight line DE , 3. The point B shall coincide with the point E , because AB is equal to DE ...
... AC , equal to the two sides DE , DF , each to each , viz . AB equal to DE , and AC equal to DF . 2. And the angle ... straight line AB on the straight line DE , 3. The point B shall coincide with the point E , because AB is equal to DE ...
Σελίδα 12
... straight line BC on EF , 3. The point C shall A coincide with the point F , because BC is equal to EF . ( hyp . ) 4. Therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF . B CE G 5. For if the base BC coincides ...
... straight line BC on EF , 3. The point C shall A coincide with the point F , because BC is equal to EF . ( hyp . ) 4. Therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF . B CE G 5. For if the base BC coincides ...
Σελίδα 13
... straight line CD . ( I. 9. ) Then AB shall be cut into two equal parts in the point D. Proof . - 1 . Because AC is equal to CB ( const . ) , and CD common to the two tri- A angles ACD , BCD ; D B 2. The two sides AC , CD , are equal to ...
... straight line CD . ( I. 9. ) Then AB shall be cut into two equal parts in the point D. Proof . - 1 . Because AC is equal to CB ( const . ) , and CD common to the two tri- A angles ACD , BCD ; D B 2. The two sides AC , CD , are equal to ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC and CB adjacent angles angle ABC angle AGH angle BAC angle BCD angle EAB angle EDF angle equal angles CBA base BC BC is equal bisected circle ABC circumference Conclusion Conclusion.-Therefore const Construction.-1 Demonstration.-1 describe the circle diameter double equal angles equal to CD equiangular exterior angle given circle given point given rectilineal angle given straight line Given.-Let ABCD gnomon greater Hypothesis inscribed interior and opposite isosceles triangle less opposite angle parallel to CD parallelogram perpendicular point F produced Q. E. D. PROPOSITION rectangle AB BC rectangle AE rectangle contained rectilineal figure References-Prop remaining angle required to describe right angles segment semicircle Sequence side BC square on AC straight line AC straight line drawn touches the circle triangle ABC triangle DEF twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 25 - 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.
Σελίδα 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 99 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 4 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 66 - ... 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...
Σελίδα 65 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 32 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 58 - 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...
Σελίδα 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 33 - The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel.