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

### Inni boken

Side 8

but the straight line c is

each of them equal to AV ; wherefore the straight line AE is equal to c ( Ax . 1 . ) ,

and from AB , the greater of two straight lines , a part A E has been cut off equal to

...

but the straight line c is

**likewise**equal to AD ( Constr . ) ; whence A E and c areeach of them equal to AV ; wherefore the straight line AE is equal to c ( Ax . 1 . ) ,

and from AB , the greater of two straight lines , a part A E has been cut off equal to

...

Side 10

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

be ...

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 . If itbe ...

Side 11

to one another , but the angle ECD is greater than the angle BCD ; wherefore the

angle FDC is

greater than the angle BCD . Again , because co is equal to do , the angle bbc is

...

to one another , but the angle ECD is greater than the angle BCD ; wherefore the

angle FDC is

**likewise**A B greater than BCD ; much more then is the angle Bdcgreater than the angle BCD . Again , because co is equal to do , the angle bbc is

...

Side 12

that have their sides which are terminated in one extremity of the base equal to

one another , and

impossible ( 1 . 7 . ) ; therefore , if the base BC coincides with the base EF ; the ...

that have their sides which are terminated in one extremity of the base equal to

one another , and

**likewise**their sides terminated in the other extremity : But this isimpossible ( 1 . 7 . ) ; therefore , if the base BC coincides with the base EF ; the ...

Side 78

to a right angle : But ABF is

equal to the angles BAD , ABD : Take from these equals the common angle ABD ;

therefore the remaining angle DBF is equal to the angle BAD , which is in the ...

to a right angle : But ABF is

**likewise**a right angle ; there . E fore the angle ABF isequal to the angles BAD , ABD : Take from these equals the common angle ABD ;

therefore the remaining angle DBF is equal to the angle BAD , which is in the ...

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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.