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

### Inni boken

Side 70

Take F the centre of the circle ABCD : And , first , let the segment BAED be

greater than a

centre , and the angle Bad at the circumference , and that they have the same

part of ...

Take F the centre of the circle ABCD : And , first , let the segment BAED be

greater than a

**semicircle**, and join BF , FD : And because the angle BFD is at thecentre , and the angle Bad at the circumference , and that they have the same

part of ...

Side 73

AC , the segment ABC is a

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 ...

AC , the segment ABC is a

**semicircle**; but if the angles a BD , BAD are not equalto 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 77

F In a circle , the angle in a

greater than a

less than a

F In a circle , the angle in a

**semicircle**is a right angle ; but the angle in a segmentgreater than a

**semicircle**is less than a right angle ; and the angle in a segmentless than a

**semicircle**is greater than a right angle . Let ABCD be a circle , of ... Side 79

AB in F , and C from the centre F , at the distance FB , describe the

AHB ; therefore the angle Ahb in a

angle at C. But , if the angle c be not a right angle , at the point A , in the straight

line A B ...

AB in F , and C from the centre F , at the distance FB , describe the

**semicircle**AHB ; therefore the angle Ahb in a

**semicircle**is ( 111. 31. ) equal to the rightangle at C. But , if the angle c be not a right angle , at the point A , in the straight

line A B ...

Side 105

If a

quadrantal arc a radius be drawn ; the part of this radius intercepted between the

quadrant and

If a

**semicircle**be described on the side of a quadrant , and from any point in thequadrantal arc a radius be drawn ; the part of this radius intercepted between the

quadrant and

**semicircle**, is equal to the perpendicular let fall from the same ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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.