## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 páginas |

### Dentro del libro

Resultados 1-5 de 11

Página 24

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**equal**A E toit ( Hyp . ) , which is impossible : therefore AB and CD being pro- C duced do not meet towards B , D. In like manner it may be demon-**F B**strated that they do not meet towards AC ; but those straight lines which meet ... Página 37

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**equal**to the squares described upon the sides which contain the right angle . Let ABC be a right angled triangle ...**FB**, BC , each to each , and the angle DBA**equal**to the angle FBC ; therefore the base AD is**equal**( 1. 4. ) to the base ... Página 56

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**equal**to DF ; wherefore DF is greater than DE , the less than the greater , which is impossible : Therefore the ...**FB**, and FE common to the two triangles AFE , BFE , there are two sides in the one**equal**to two sides in the other , and ... Página 58

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**equal to FB**: Also because F is the centre of the circle CDE , CF is equal to FE : And CF was shown**equal to FB**; therefore FE is**equal to FB**, the less to the greater , which is impossible ; wherefore F is not the centre of the circles ... Página 64

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**Equal**straight lines in a circle are equally distant from the centre ; and those which are equally distant from the ...**FB**, and AB double of AF . For the same reason , CD is double of CG : And AB is**equal**to CD ( Hyp . ) ; therefore ...### Otras ediciones - Ver todas

The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |

The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |

### Términos y frases comunes

ABCD adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle CAB angle EDF angle equal angles CBA base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AB straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle

### Pasajes populares

Página 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...

Página 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Página 20 - If two triangles have two sides of the one equal to two sides of the...

Página 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.