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

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Side 66

Let ABC be a circle , the centre of which is D , and the diameter AB : the straight

For , if it does not , let it fall , if possible , within the circle , as AC , and draw DC to

...

Let ABC be a circle , the centre of which is D , and the diameter AB : the straight

**line drawn**at right angles to A B from its extremity A , shall fall without the circle .For , if it does not , let it fall , if possible , within the circle , as AC , and draw DC to

...

Side 90

If a perpendicular be

perpendicular is at equal distances from the extremities of the

straight

that ...

If a perpendicular be

**drawn**bisecting a given straight**line**, any point in thisperpendicular is at equal distances from the extremities of the

**line**. 20. Of allstraight

**lines**which can be**drawn**from a given point to an indefinite straight**line**,that ...

Side 94

To bisect a trapezium ( 1st ) by a

by a

figure of any number of sides being given , to find an equal rectilineal figure

which ...

To bisect a trapezium ( 1st ) by a

**line drawn**from one of its angular points , ( 20 )by a

**line drawn**from a given point in one of its sides . 20. A plane rectilinealfigure of any number of sides being given , to find an equal rectilineal figure

which ...

Side 97

intersect , the line PQ will be equal to the sum of the lines B P and co . 14. The

difference of the angles at the base of a triangle is double the angle contained by

a

bisecting ...

intersect , the line PQ will be equal to the sum of the lines B P and co . 14. The

difference of the angles at the base of a triangle is double the angle contained by

a

**line drawn**from the vertex perpendicular to the base , and another linebisecting ...

Side 104

Euclides, Thomas Tate. horizontal

flag - staff appear under the greatest angle ? 37. Given the vertical angle , the

difference of the two sides containing it , and the difference of the segments of the

...

Euclides, Thomas Tate. horizontal

**line**,**drawn**from the foot of the tower , will theflag - staff appear under the greatest angle ? 37. Given the vertical angle , the

difference of the two sides containing it , and the difference of the segments of the

...

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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.