## Euclid's Elements of geometry, books i. ii. iii. iv |

### Inni boken

Resultat 1-5 av 23

Side 4

... or to be

... or to be

**proved**, as a theorem . A problem proposes something to be done , such as the construction of a figure . A theorem makes an assertion , the truth of which it proposes to demonstrate . A postulate is a problem so simple that ... Side 8

But the point B was

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 , two straight ... Side 9

And FC was

And FC was

**proved**to be equal to GB . 8. Therefore the two sides BF , FC , are equal to the two sides CG , GB , each to each . 9. And the angle BFC was**proved**equal to the angle CGB . 10. Therefore the triangles BFC , CGB , are equal ... Side 10

( ax . 9. ) 4. Therefore the angle ADC is also greater than BCD . 5. Much more then is the angle BDC greater than BCD . Q. E. D. is an abbreviation for quod erat demonstrandum , that is , “ which was to be shown or

( ax . 9. ) 4. Therefore the angle ADC is also greater than BCD . 5. Much more then is the angle BDC greater than BCD . Q. E. D. is an abbreviation for quod erat demonstrandum , that is , “ which was to be shown or

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### Vanlige uttrykk og setninger

ABCD angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisected BOOK centre circle ABC circumference coincide common Conclusion Conclusion.—Therefore const Construction Construction.-1 Demonstration Demonstration.-1 describe diameter distance divided double draw drawn equal exterior angle extremities fall figure four given circle given point given straight line greater half Hypothesis Hypothesis.—Let impossible inscribed join less manner meet opposite angles parallel parallelogram pass perpendicular produced proved Q. E. D. PROPOSITION reason rectangle contained rectilineal figure References-Prop right angles segment semicircle Sequence.—The shown sides square on AC straight line AC Take third touches the circle triangle ABC twice the rectangle whole

### Populære avsnitt

Side 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.

Side 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.

Side 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.

Side 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...

Side 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...

Side 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.

Side 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.

Side 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...

Side 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 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.