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

### Inni boken

Resultat 1-5 av 15

Side 8

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**triangle ABC**to the triangle DEF ; and the other angles , to which the equal sides are op- posite , shall be equal each to each , viz . the**angle ABC**to the angle DEF , and the**angle ACB**to DFE . B CE For , if the**triangle ABC**be ... Side 9

... angles upon the other side of the base shall be equal . Let ABC be an Isosceles triangle , of which the side A B is equal to AC , and let the straight lines AB , AC be produced to D and E , the

... angles upon the other side of the base shall be equal . Let ABC be an Isosceles triangle , of which the side A B is equal to AC , and let the straight lines AB , AC be produced to D and E , the

**angle ABC**shall be equal to the**angle ACB**, ... Side 10

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**ACB**; the side A B is also equal to the side AC . For , if AB be not equal ...**ACB**, DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two ...**angle**BDC is equal ( 1.5 . ) to the**angle**10 EUCLID'S ELEMENTS . Side 11

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**angle ACB**; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 1. 5. ) to one another , but the angle ECD is greater than the angle ... Side 12

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**angle**BAC coincides with the**angle**EDF , and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c ...**ACB**by the straight line CD . cut into two equal parts in the point D. Because AC is equal to CB , and CD common to the two ...### 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 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

### 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.