## 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 17

two right angles . Let ABC be any triangle ; any two of A its angles together are

less than two right angles . Produce BC to D ; and because ACD is the exterior ...

**Q. E. D. PROP**. XVII . THEOR . Any two angles of a triangle are together less thantwo right angles . Let ABC be any triangle ; any two of A its angles together are

less than two right angles . Produce BC to D ; and because ACD is the exterior ...

Side 18

PROP . XIX . THEOR . The greater angle of every triangle is subtended by the

greater side , or has the greater side opposite to it ...

Any two sides of a triangle are together greater than the third side . D Let ABC be

a ...

PROP . XIX . THEOR . The greater angle of every triangle is subtended by the

greater side , or has the greater side opposite to it ...

**Q.E.D. PROP**. XX . THEOR .Any two sides of a triangle are together greater than the third side . D Let ABC be

a ...

Side 31

same parallels , are equal to one another . Let the triangles ABC , DEF be upon

equal bases BC , EF , and between the same parallels BF , AD : The triangle ABC

...

**Q.E.D. PROP**. XXXVIII . THEOR . Triangles upon equal bases , and between thesame parallels , are equal to one another . Let the triangles ABC , DEF be upon

equal bases BC , EF , and between the same parallels BF , AD : The triangle ABC

...

Side 61

more than two points . If it be possible , let the circumference FAB cut the cirK

cumference DEF in more than two А points , viz BOOK III . 61 PROPS . IX . X.

**Q. E. D. PROP**. X. THEOR . One circumference of a circle cannot cut another inmore than two points . If it be possible , let the circumference FAB cut the cirK

cumference DEF in more than two А points , viz BOOK III . 61 PROPS . IX . X.

Side 75

equal straight lines cut off equal circumferences , the greater equal to the greater

, and the less to the less . Let ABC , DEF be equal circles , and BC , EF equal ...

**Q.E.D.**Wherefore in equal circles ,**PROP**. XXVIII . THEOR . In equal circles ,equal straight lines cut off equal circumferences , the greater equal to the greater

, and the less to the less . Let ABC , DEF be equal circles , and BC , EF equal ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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 to FB equilateral exterior angle extremity figure fore four given point given straight line greater half impossible interior isosceles triangle join less Let ABC Let the straight likewise 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 side bc sides squares of AC straight lines 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.