## 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 19

Produce BD to E ; and because two sides of a triangle are greater than the

side , the two sides BA , A E of the triangle ABE are greater than BE , to each of

these add EC ; therefore the sides BA , AC are greater than BE , EC : Again ...

Produce BD to E ; and because two sides of a triangle are greater than the

**third**side , the two sides BA , A E of the triangle ABE are greater than BE , to each of

these add EC ; therefore the sides BA , AC are greater than BE , EC : Again ...

Side 22

AB to DE , and AC to DF ; and the

a B be not equal to DE , one of them must be the greater . Let B E A B be the

greater of the two , and make Bg equal to DE , and join GC ; therefore , because

BG ...

AB to DE , and AC to DF ; and the

**third**angle BAC to the**third**angle EDF . For , ifa B be not equal to DE , one of them must be the greater . Let B E A B be the

greater of the two , and make Bg equal to DE , and join GC ; therefore , because

BG ...

Side 23

to the base DF , and the

sides which are D opposite to equal angles in each triangle be equal to one

another , viz . AB LO DE ; likewise in this case , the other sides shall be equal ,

AC to DF ...

to the base DF , and the

**third**angle BAC to the**third**angle EDF . Next , let thesides which are D opposite to equal angles in each triangle be equal to one

another , viz . AB LO DE ; likewise in this case , the other sides shall be equal ,

AC to DF ...

Side 85

is one

angle CBD is one

bisected by BE , the angles DBE and EBA are each of them equal to one

a right ...

is one

**third**of two right angles , or two thirds of the right angle ABC ; therefore theangle CBD is one

**third**of the right angle CBA ; but since the angle DBA isbisected by BE , the angles DBE and EBA are each of them equal to one

**third**ofa right ...

Side 87

12. Given the hypotenuse of a right - angled triangle , and the difference of the

two acute angles , to construct the triangle . 13. To construct a right - angled

triangle , having given the hypotenuse , and one of the acute angles equal to one

12. Given the hypotenuse of a right - angled triangle , and the difference of the

two acute angles , to construct the triangle . 13. To construct a right - angled

triangle , having given the hypotenuse , and one of the acute angles equal to one

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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.