## 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 24

For , if it be not parallel , AB and cd being

D , or towards A , C ; let them be

therefore GEF is a triangle , and its exterior angle A EF is greater ( 1. 16. ) ...

For , if it be not parallel , AB and cd being

**produced**, shall meet either towards B ,D , or towards A , C ; let them be

**produced**and meet towards B , D in the point g ;therefore GEF is a triangle , and its exterior angle A EF is greater ( 1. 16. ) ...

Side 43

If a straight line be bisected , and

by the whole line thus

square of half the line bisected , is equal to the square of the straight line , which

...

If a straight line be bisected , and

**produced**to any point ; the rectangle containedby the whole line thus

**produced**, and the part of it**produced**, together with thesquare of half the line bisected , is equal to the square of the straight line , which

...

Side 47

If a straight line be bisected , and

line thus

double of the square of half the line bisected , and of the square of the line made

up of ...

If a straight line be bisected , and

**produced**to any point , the square of the wholeline thus

**produced**, and the square of the part of it**produced**, are togetherdouble of the square of half the line bisected , and of the square of the line made

up of ...

Side 50

In obtuse angled triangles , if a perpendicular be drawn from any of the acute

angles to the opposite side

obtuse angle is greater than the squares of the sides containing the obtuse angle

, by ...

In obtuse angled triangles , if a perpendicular be drawn from any of the acute

angles to the opposite side

**produced**, the square of the side subtending theobtuse angle is greater than the squares of the sides containing the obtuse angle

, by ...

Side 107

If a semicircle be inscribed in a right - angled triangle , so as to touch the

hypotenuse and perpendicular , and from the extremity of its diameter a line be

drawn through the point of contact to meet the perpendicular

If a semicircle be inscribed in a right - angled triangle , so as to touch the

hypotenuse and perpendicular , and from the extremity of its diameter a line be

drawn through the point of contact to meet the perpendicular

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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.