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

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Side 6

If equals be

are double of the same , are equal to one another . VII . Things which are halves

of the same , are equal to one another . VIII . Magnitudes which coincide with one

...

If equals be

**taken**from unequals , th remainders are unequal . VI . Things whichare double of the same , are equal to one another . VII . Things which are halves

of the same , are equal to one another . VIII . Magnitudes which coincide with one

...

Side 59

If any point be

circumference , whereof one passes through the centre ; of those which fall upon

the concave circumference , the greatest is that which passes through the centre

...

If any point be

**taken**without a circle , and straight lines be drawn from it to thecircumference , whereof one passes through the centre ; of those which fall upon

the concave circumference , the greatest is that which passes through the centre

...

Side 61

... more remote , which is impossible . If , therefore , any point , & c . Q. E. D.

PROP . IX . PROB . If a point be

than two equal straight lines to the circumference , that point is the centre of the

circle .

... more remote , which is impossible . If , therefore , any point , & c . Q. E. D.

PROP . IX . PROB . If a point be

**taken**within a circle , from which there fall morethan two equal straight lines to the circumference , that point is the centre of the

circle .

Side 89

The diagonals of a parallelogram bisect one another . 5. The diagonals of a

square cut each other at right angles . 6. The three sides of a triangle

together exceed the double of any one side , and are less than the double of any

two sides ...

The diagonals of a parallelogram bisect one another . 5. The diagonals of a

square cut each other at right angles . 6. The three sides of a triangle

**taken**together exceed the double of any one side , and are less than the double of any

two sides ...

Side 97

If in two opposite sides of a parallelogram two points be

those sides equidistant from two opposite angles of the figure , and if two other

points be likewise

same ...

If in two opposite sides of a parallelogram two points be

**taken**, one in each ofthose sides equidistant from two opposite angles of the figure , and if two other

points be likewise

**taken**, in the two other opposite sides , equidistant from thesame ...

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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.