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

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Side 8

But the point B coincides with the point E ; wherefore the

with the base EF , because the point B coinciding with E , and c with F , if the

space ...

But the point B coincides with the point E ; wherefore the

**base Bc**shall coincidewith the base EF , because the point B coinciding with E , and c with F , if the

**base Bc**does not coincide with the base EF , two straight lines would inclose aspace ...

Side 21

AB equal to DE , and AC to DF ; but the angle BAC greater than the angle EDF ;

the

the side which is not greater than the other , and at the point n , in the straight ...

AB equal to DE , and AC to DF ; but the angle BAC greater than the angle EDF ;

the

**base Bc**is also greater than the base EF . Of the two sides DE , DF , let DE bethe side which is not greater than the other , and at the point n , in the straight ...

Side 22

For , if it be not greater , it must either be equal to it , or less ; but the angle Bac is

not equal to the angle EDF , because then the

EF ; but it is not , therefore the angle Bac is not equal to the angle EDF ; neither ...

For , if it be not greater , it must either be equal to it , or less ; but the angle Bac is

not equal to the angle EDF , because then the

**base BC**would be equal ( 1. 4. ) toEF ; but it is not , therefore the angle Bac is not equal to the angle EDF ; neither ...

Side 29

BCA in one , equal to two angles BCD , CBD in the other , each to each , and one

side bc common to the two triangles ... Let the parallelograms ABCD , EBCF ( see

the 2d and 3d figures ) be upon the same

BCA in one , equal to two angles BCD , CBD in the other , each to each , and one

side bc common to the two triangles ... Let the parallelograms ABCD , EBCF ( see

the 2d and 3d figures ) be upon the same

**base BC**, and between the same ... Side 30

to the interior E A B , therefore the base EB is equal to the base FC , and the

triangle EAB equal ( 1. ... to ABCD , because it is upon the same

between the same parallels BC , AD : For the like reason , the parallelogram

EFGH is ...

to the interior E A B , therefore the base EB is equal to the base FC , and the

triangle EAB equal ( 1. ... to ABCD , because it is upon the same

**base BC**, andbetween the same parallels BC , AD : For the like reason , the parallelogram

EFGH is ...

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The first three books of Euclid's Elements of geometry, with theorems and ... Euclides Uten tilgangsbegrensning - 1851 |

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

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.