Euclid's Elements of geometry, books i. ii. iii. iv1862 |
Αναζήτηση στο βιβλίο
Σελίδα 6
... F. ( post . 2. ) 4. From the centre B , at the dis- tance BC , describe the circle CGH , meeting DF in G. ( post . 3 ... point B is the centre of the circle CGH , BC is equal to BG . ( def . 15. ) 2. Because the point D is the ...
... F. ( post . 2. ) 4. From the centre B , at the dis- tance BC , describe the circle CGH , meeting DF in G. ( post . 3 ... point B is the centre of the circle CGH , BC is equal to BG . ( def . 15. ) 2. Because the point D is the ...
Σελίδα 7
... point C shall coincide with the point F , because the straight line AC is equal to DF . ( hypothesis . ) * Q. E. F. is an abbreviation for quod erat faciendum , that is , “ which was to be done . " 6. But the point B was proved to ...
... point C shall coincide with the point F , because the straight line AC is equal to DF . ( hypothesis . ) * Q. E. F. is an abbreviation for quod erat faciendum , that is , “ which was to be done . " 6. But the point B was proved to ...
Σελίδα 8
Euclides. 6. But the point B was proved to coincide with the point E. 7. Therefore the base BC shall coincide with the base EF . 8. Because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF ...
Euclides. 6. But the point B was proved to coincide with the point E. 7. Therefore the base BC shall coincide with the base EF . 8. Because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF ...
Σελίδα 12
... point B may be on E , and the straight line BC on EF , 3. The point C shall A coincide with the point F , because BC is equal to EF . ( hyp . ) D G 4. Therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF . B CE 5 ...
... point B may be on E , and the straight line BC on EF , 3. The point C shall A coincide with the point F , because BC is equal to EF . ( hyp . ) D G 4. Therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF . B CE 5 ...
Σελίδα 14
... F 3. And the base DF is equal to the base EF ; ( const . ) 4. Therefore the angle DCF is equal to the angle ECF ... point C in the given straight line AB , a straight line FC has been drawn at right angles to AB . Q. E. F. ...
... F 3. And the base DF is equal to the base EF ; ( const . ) 4. Therefore the angle DCF is equal to the angle ECF ... point C in the given straight line AB , a straight line FC has been drawn at right angles to AB . Q. E. F. ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC and CD 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 const Construction Construction.-1 Demonstration Demonstration.-1 describe the circle diameter double equal angles equal to CD exterior angle given circle given point given straight line gnomon greater Hypothesis Hypothesis.-Let inscribed interior and opposite isosceles triangle join less Let ABC opposite angle parallel to CD parallelogram perpendicular produced PROPOSITION 13 Q. E. D. PROPOSITION rectangle AD DC 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 THEOREM 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.