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

### Inni boken

Resultat 1-5 av 38

Side 22

Result ... A C , BC , AB are all equal to one another . Wherefore the

Result ... A C , BC , AB are all equal to one another . Wherefore the

**triangle A B C**is equilateral , and it is described on the given straight line A B. Q. E. F. Proof ( with contracted syllogisms , in the words of Euclid ) . Side 23

Wherefore the

Wherefore the

**triangle A B C**is equilateral , and it is described on the given straight line A B. Q. E. F. EXERCISES . - I . Describe an equilateral triangle having each of its sides double the given straight line O P. 0 II . Side 32

( a ) On A B describe an equilateral

( a ) On A B describe an equilateral

**triangle ABC**( Euc . I. I shows how . ) ( 6 ) Bisect the angle ' A CB by the straight line CD , meeting AB at D. ( Euc . I. 9 shows how to do this . ) Then the line A B shall be bisected at the point ... Side 49

The line A B , standing on the line CD , and forming the two

The line A B , standing on the line CD , and forming the two

**angles A B C**, A B D. B Required . — To prove either( a ) That**angles ABC**, ABD are two right angles , or ( 6 ) That**angles ABC**, A B D are together equal to two right angles ... Side 50

( 6 ) Let us assume that

( 6 ) Let us assume that

**angle A B C**is not equal to angle A BD , as in this figure . For the purpose of proof draw EB at right angles to CD . In this figure we have now five angles . D B Two angles CBA , ABD formed by the line A B ...### 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.