## 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 22

AB equal to DE , and AC to DF ; but the base cb is greater than the base EF ; the

angle bac is likewise greater than the ... viz . either the sides adjacent to the

...

AB equal to DE , and AC to DF ; but the base cb is greater than the base EF ; the

angle bac is likewise greater than the ... viz . either the sides adjacent to the

**equal angles**, or the sides opposite to**equal angles**in each ; then shall the other...

Side 23

А and the other

sides are opposite ; therefore the

is , by the hypothesis ,

А and the other

**angles**to the other**angles**, each to each , to which the**equal**sides are opposite ; therefore the

**angle**GCB is**equal**to the**angle**DFE ; but DfEis , by the hypothesis ,

**equal**to the**angle**BCA ; wherefore aso the**angle**BCG is ... Side 71

THEOR . The opposite

together

circle ABCD ; any two of its opposite

.

THEOR . The opposite

**angles**of any quadrilateral figure inscribed in a circle , aretogether

**equal**to two right**angles**. Let ABCD be a quadrilateral figure in thecircle ABCD ; any two of its opposite

**angles**are together**equal**to two right**angles**.

Side 73

AC , the segment ABC is a semicircle ; but if the

to one another , at the point A , in the straight line BA , make ( 1. 23. ) the

BAE

AC , the segment ABC is a semicircle ; but if the

**angles**a BD , BAD are not**equal**to one another , at the point A , in the straight line BA , make ( 1. 23. ) the

**angle**BAE

**equal**to the**angle**ABD , and produce bd , if necessary , to e , and join Ec ... Side 86

the

the

E. 1. 6. ) AE is

...

the

**angles**DAC and ADE are**equal**; but ( by constr . ) the**angle**EaD is**equal**tothe

**angle**DAC ; therefore the**angle**ADE is**equal**to the**angle**EAD ; wherefore (E. 1. 6. ) AE is

**equal**to ED . For the same reason FB is**equal**to FD . But dE being...

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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.