## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |

### Inni boken

Resultat 1-5 av 9

Side 6

Magnitudes which

Magnitudes which

**coincide**with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot inclose a space . XI . Side 8

and AB

and AB

**coinciding**with DE , AC shall**coincide**with DF because the angle Bac is equal to the angle EDF ( Hyp . ) ; wherefore also the point c shall**coincide**with the point F , because the straight line ac is equal to DF ( Hyp . ) . Side 11

For if the triangle ABC be applied to DEF , so that the point B be on E , and the straight line bc upon EF ; the point c shall also

For if the triangle ABC be applied to DEF , so that the point B be on E , and the straight line bc upon EF ; the point c shall also

**coincide**with the B point F , because Bc is equal to EF ( Hyp . ) ; therefore BC**Coinciding**with EF ... Side 12

therefore , if the base Bc'

therefore , if the base Bc'

**coincides**with the base EF ; the sides BA , AC cannot but**coincide**with the sides ED , DF ; wherefore likewise the angle BAC**coincides**with the angle EDF , and is equal ( Ax . 8. ) to it . Side 53

“ This is not a definition but a theorem , the truth of which is evident ; for , if the circles be applied to one another , so that their centres

“ This is not a definition but a theorem , the truth of which is evident ; for , if the circles be applied to one another , so that their centres

**coincide**, the circles must likewise**coincide**, since the straight lines from the centres ...### Hva folk mener - Skriv en omtale

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### 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 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 lines AC 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 A B 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.