## 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 30

that is , the

to ...

that is , the

**parallelogram**ABCD is equal to the**parallelogram**EBCF . Therefore ,**parallelograms**upon the same base , & c . Q. E. D. PROP . XXXVI . THEOR .**Parallelograms**upon equal bases , and between the same parallels , are equalto ...

Side 33

С the same base BC , and between the same D E parallels BC , AE ; the

ABC is equal ( 1. 37. ) to the triangle EBC , because they are upon the same base

BC , and ...

С the same base BC , and between the same D E parallels BC , AE ; the

**parallelogram**ABCD is double of the triangle EBC . Join Ac ; then the triangleABC is equal ( 1. 37. ) to the triangle EBC , because they are upon the same base

BC , and ...

Side 34

The complements of the

which the diameter is AC , and EH , Fg the

is ...

The complements of the

**parallelogram**which are about the diameter of any**parallelogram**, are equal to one another . Let ABCD be a**parallelogram**, ofwhich the diameter is AC , and EH , Fg the

**parallelograms**about A H D AC , thatis ...

Side 36

to ml : and KM , FL are parallels ; wherefore KFLM is a

because the triangle ABD is equal to the

to the

...

to ml : and KM , FL are parallels ; wherefore KFLM is a

**parallelogram**; andbecause the triangle ABD is equal to the

**parallelogram**HF , and the triangle dbcto the

**parallelogram**Gm ; the whole rectilineal figure ABCD is equal to the whole...

Side 90

Euclides, Thomas Tate. either pair of opposite sides , are together half of the

is less , or greater , than the half of the vertical angle , accordingly as the triangle

is a ...

Euclides, Thomas Tate. either pair of opposite sides , are together half of the

**parallelogram**. 18. The angle at the base of an isosceles triangle is equal to , oris less , or greater , than the half of the vertical angle , accordingly as the triangle

is a ...

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### 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.