## First principles of Euclid: an introduction to the study of the first book of Euclid's Elements |

### Inni boken

Resultat 1-5 av 9

Side 15

7. Things which are halves of the same thing are equal to one another . 8. Magnitudes which

7. Things which are halves of the same thing are equal to one another . 8. Magnitudes which

**coincide**with one another are equal to one another . 8a . ( Not given by Euclid , but assumed Axioms . 15 AXIOMS. Side 16

Lines and angles which are equal to one another ,

Lines and angles which are equal to one another ,

**coincide**with one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . 11. All right angles are equal to each other . 12. Side 17

When lines

When lines

**coincide**their points**coincide**( assumed as an axiom ) . A B and CD**coincide**( 1st conclusion ( a ) become a premiss ) . ( b ) .: The points of A B and CD**coincide**( 2nd conclusion ) 3rd Syllogism . Side 28

so that the point A falls upon the point D , and the line A B on the line D E. Then , if the line AC

so that the point A falls upon the point D , and the line A B on the line D E. Then , if the line AC

**coincide**with the line DF , the angles are equal . If the line AC fall within the angle E DF , the angle B A C is less than EDF . Side 71

Let the triangle A B C be applied to placed upon ) the triangle DEF , so that the point A falls upon the point B ; and the line Ā B falls Then ( a ) The point B shall

Let the triangle A B C be applied to placed upon ) the triangle DEF , so that the point A falls upon the point B ; and the line Ā B falls Then ( a ) The point B shall

**coincide**with the point E because AB is equal to DE ( Axiom 8a ) .### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

A B is equal ABCD angle A B C angle A CD angle ABC angle AGH angle B A C angle BAC angle BCD angle contained angle EDF angles equal assumed Axiom Axiom 2a base B C bisected called centre circle circumference coincide conclusion Construction definition describe draw enunciations of Euc equal angles equal to A B equal to angle equilateral triangle EXERCISE exterior angle fall figure given point given straight line Given.-The greater than angle Hence included angle Join less Let us suppose letters line A B major premiss meet parallel parallelogram Particular Enunciation produced Proof proposition prove that angle Repeat.-The enunciations Required.—To prove right angles side A C sides equal square standing Syllogism THEOREM Euclid thing third triangle ABC unequal whole

### Populære avsnitt

Side 83 - 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...

Side 18 - 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 66 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Side 34 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.

Side 94 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.

Side 88 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 104 - If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.

Side 142 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

Side 51 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Side 133 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.