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

### Inni boken

Resultat 1-5 av 5

Side 27

to two right angles ; therefore also the angles CBA , BAC , ACB are equal to two

right angles . Wherefore if a D . side of a triangle , & c . Q . E . D . CoR . 1 . All the

interior angles of any rectilineal figure , together with

...

to two right angles ; therefore also the angles CBA , BAC , ACB are equal to two

right angles . Wherefore if a D . side of a triangle , & c . Q . E . D . CoR . 1 . All the

interior angles of any rectilineal figure , together with

**four**right angles , are equal...

Side 28

B PROP . XXXIII . THEOR . The straight lines which join the extremities of two

equal and parallel straight lines , towards the same parts , are also themselves ...

**four**right angles ; therefore all the exterior angles are equal to**four**right angles .B PROP . XXXIII . THEOR . The straight lines which join the extremities of two

equal and parallel straight lines , towards the same parts , are also themselves ...

Side 45

If a straight line be divided into any two parts ,

by the whole line , and one of the parts , together with the square of the other part

, is equal to the square of the straight line wħich is made up of the whole and ...

If a straight line be divided into any two parts ,

**four**times the rectangle containedby the whole line , and one of the parts , together with the square of the other part

, is equal to the square of the straight line wħich is made up of the whole and ...

Side 96

If in the sides of a square , at equal distances from the

points be taken , one in each side ; the figure contained by the straight lines

which join them shall also be a square . 8. If

without ...

If in the sides of a square , at equal distances from the

**four**angles ,**four**otherpoints be taken , one in each side ; the figure contained by the straight lines

which join them shall also be a square . 8. If

**four**straight lines cut each other ,without ...

Side 99

... two lines joining the bisections of the opposite sides . 17. The squares of the

diagonals of a trapezium are together less than the squares of the

... two lines joining the bisections of the opposite sides . 17. The squares of the

diagonals of a trapezium are together less than the squares of the

**four**sides , by**four**times the square of the line joining the points of bisection of the diagonals .### 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.