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

### Inni boken

Resultat 1-5 av 61

Side 13

But in both cases a proof is

But in both cases a proof is

**required**. Thus in a problem , it is not enough to do what is**required**to be done . We must also**prove**, by syllogisms , that it is done . Every proposition , whether problem or theorem , consists of two ... Side 16

Such a Chain of Syllogisms is used in

Such a Chain of Syllogisms is used in

**proving**the truth of the following proposition . Given . - The line A B equal to the line CD .**Required**. To**prove**that if the line A B be placed upon the line CD , so that the point A falls upon ... Side 19

The line A E shall be equal to C. ( If AE be equal to C , we have done what was required — that is , cut off from A B a part equal to C. But it is

The line A E shall be equal to C. ( If AE be equal to C , we have done what was required — that is , cut off from A B a part equal to C. But it is

**necessary to prove**that AE is equal to C. ) Ist Proof ( with syllogisms given in full ) ... Side 21

**Required**. To describe an equilateral triangle on AB . Construction . B ( a ) From the centre A , at the distance AB ... CB , to A and B. B Then A CB shall be an equilateral triangle ( now we must**prove**that A B C is equilateral ) . Side 23

Describe two equilateral triangles , one on each side of the given line and

Describe two equilateral triangles , one on each side of the given line and

**prove**that the five sides are all ... A , B , C , of which A and B are greater than C : A and C B are greater than B : B and C с are greater than A.**Required**.### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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.