## 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 8

For , if the triangle ABC be applied to DEF , so that the point A may be on D , and

the straight line AB upon DE ; the point B shall

AB is equal to DE ( Hyp . ) ; and AB coinciding with DE , AC shall

For , if the triangle ABC be applied to DEF , so that the point A may be on D , and

the straight line AB upon DE ; the point B shall

**coincide**with the point E , becauseAB is equal to DE ( Hyp . ) ; and AB coinciding with DE , AC shall

**coincide**with ... Side 11

therefore BC Coinciding with EF , BA and ac shall

if the base BC

with the sides ED , FD , but have a different situation as EG , FG ...

therefore BC Coinciding with EF , BA and ac shall

**coincide**with ED and DF ; for ,if the base BC

**coincides**with the base EF , but the sides BA , CA do not**coincide**with the sides ED , FD , but have a different situation as EG , FG ...

Side 12

therefore , if the base BC

but

with the angle EDF , and is equal ( Ax . 8 . ) to it . Therefore if two triangles , & c .

therefore , if the base BC

**coincides**with the base EF ; the sides BA , AC cannotbut

**coincide**with the sides ED , DF ; wherefore likewise the angle BAC**coincides**with the angle EDF , and is equal ( Ax . 8 . ) to it . Therefore if two triangles , & c .

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

likewise

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 mustlikewise

**coincide**, since the straight lines from the centres are equal . ” IL . Go VI . Side 72

Therefore , there cannot be two similar segments of a circle upon the same side

of the same line , which do not

segments of circles upon equal straight lines are equal to one another . Let A E B

...

Therefore , there cannot be two similar segments of a circle upon the same side

of the same line , which do not

**coincide**. Q. E. D. PROP . XXIV . THEOR . Similarsegments of circles upon equal straight lines are equal to one another . Let A E B

...

### 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 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 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 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.