## 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 47

Side 6

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**straight lines**cannot inclose a space . XI . All right angles are equal to one another . XII . " If a**straight line**...**AC**is equal ( Definition 15. ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : But ... Side 8

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**straight line**c is likewise equal to AD ( Constr . ) ; whence AE and c are each of them equal to AD ; wherefore the ...**AC**equal to the two sides DE , DF , AÅ each to each , viz . AB to DE , and**AC**A to DF ; and the angle BAC equal to ... Side 11

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**AC**, AD to E , F ; therefore , because**AC**is equal to AD in the triangle ACD , the angles ECD , FDC upon the other ...**straight line**BC upon EF ; the point c shall also coincide with the B point F , because BC is equal to EF ( Hyp . ) ; ... Side 12

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**AC**cannot but coincide with the sides ED , DF ; wherefore likewise the angle ...**straight line**AF bisects the triangle BA C. Because AD is equal to AE , and ...**straight line**AF . Which was to be done . PROP . X. PROB . A E To bisect a ... Side 16

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**straight line**AE makes C with CD the angles CEA , AED , these angles are together equal ( 1. 13. ) to two A right ...**AC**in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce**AC**to G. A B C G F Because ...### 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.