## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |

### Inni boken

Resultat 1-5 av 5

Side 9

Which was to be

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 . Let ABC be

...

Which was to be

**demonstrated**. AB is PROP . V. THEOR . The angles at the baseof 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 . Let ABC be

...

Side 16

to two right angles ; and CEA , A ED have been

right angles ; wherefore the angles CEA , A ED are equal to the angles A ED , DE

B. Take away the common angle AED , and the remaining angle cea is equal ...

to two right angles ; and CEA , A ED have been

**demonstrated**to be equal to tworight angles ; wherefore the angles CEA , A ED are equal to the angles A ED , DE

B. Take away the common angle AED , and the remaining angle cea is equal ...

Side 17

the angle ACD is greater than B A E. In the same manner , if the side bc be

bisected , it may be

acv , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. PROP .

the angle ACD is greater than B A E. In the same manner , if the side bc be

bisected , it may be

**demonstrated**that the angle BCG , that is ( 1. 15. ) , the angleacv , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. PROP .

Side 32

B с In the same manner , it can be

parallel to BC ; Ad is therefore parallel to it . Wherefore equal triangles upon , & c

. Q.E.D. PROP . XL . THBOR . A Equal triangles upon equal bases , in the same ...

B с In the same manner , it can be

**demonstrated**that no other line but ad isparallel to BC ; Ad is therefore parallel to it . Wherefore equal triangles upon , & c

. Q.E.D. PROP . XL . THBOR . A Equal triangles upon equal bases , in the same ...

Side 65

Next , if the straight lines A B , CD be equally distant from the centre , that is , if FE

be equal to EG ; AB is equal to CD : For , the same construction being made , it

may , as before , be

...

Next , if the straight lines A B , CD be equally distant from the centre , that is , if FE

be equal to EG ; AB is equal to CD : For , the same construction being made , it

may , as before , be

**demonstrated**, that AB is double of A F , and cd double of cG...

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The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |

### Vanlige uttrykk og setninger

ABCD alternate angle ABC angle ACB angle BAC angle equal base BC BC is equal bisect centre circle ABC circumference coincide common construct demonstrated describe diameter divided double draw equal angles equal to FB equilateral exterior angle extremity figure fore four given point given straight line gnomon greater impossible interior isosceles triangle join less Let ABC likewise line be drawn meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced PROP Q. E. D. PROP rectangle contained remaining angle right angles segment semicircle shown sides squares of AC straight line AC Take taken THEOR third touch touches the circle triangle ABC twice the rectangle vertex wherefore whole

### Populære avsnitt

Side 6 - 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 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 20 - If two triangles have two sides of the one equal to two sides of the...

Side 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.

Side 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.

Side 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.

Side 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 11 - 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 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.

Side 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.