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

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Resultat 1-5 av 5

Side 9

... equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle

afc to the angle AGB : And E because the

which the parts A B , AC , are equal : the remainder BF shall be equal ( Ax . 3. ) ...

... equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle

afc to the angle AGB : And E because the

**whole**AF is equal to the**whole**AG , ofwhich the parts A B , AC , are equal : the remainder BF shall be equal ( Ax . 3. ) ...

Side 34

Let ABCD be a parallelogram , of which the diameter is AC , and EH , Fg the

parallelograms about A H D AC , that is , through which AC passes , and BK , KD

the other parallelograms F which make up the

Let ABCD be a parallelogram , of which the diameter is AC , and EH , Fg the

parallelograms about A H D AC , that is , through which AC passes , and BK , KD

the other parallelograms F which make up the

**whole**figure ABCD , which are ... Side 43

to the complement , to each of these add DM ; therefore the

equal to the

equal to CB ; therefore also al is equal to DF . To each of these add ch , and the ...

to the complement , to each of these add DM ; therefore the

**whole**CM A С DB isequal to the

**whole**DF ; but cm is L H equal ( 1. 36. ) to Al , because Ac is K M мequal to CB ; therefore also al is equal to DF . To each of these add ch , and the ...

Side 44

Q. E. D. PROP . VII . THEOR . H If a straight line be divided into any two parts , the

squares of the

contained by the

Q. E. D. PROP . VII . THEOR . H If a straight line be divided into any two parts , the

squares of the

**whole**line , and one of the parts , are equal to twice the rectanglecontained by the

**whole**and that part , together with the square of the other part . Side 95

But since Pg is greater than GQ , the triangle APG is greater than AGQ , and the

triangle God is greater than GQP ; therefore , the

than the

equal ...

But since Pg is greater than GQ , the triangle APG is greater than AGQ , and the

triangle God is greater than GQP ; therefore , the

**whole**triangle DPA is greaterthan the

**whole**triangle DQA ; but it has been shown that the triangle DPA isequal ...

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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.