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

### Inni boken

Resultat 1-5 av 23

Side 7

But it has been

But it has been

**shown**that Bc is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line Al is equal to BC . Wherefore from the given ... Side 18

than the angle ACB ; but it is not ; therefore the side ac is not less than AB ; and it has been

than the angle ACB ; but it is not ; therefore the side ac is not less than AB ; and it has been

**shown**that it is not equal to AB ; therefore ac is greater than a B. Wherefore the angle , & c . Q.E.D. PROP . XX . THEOR . Side 19

... AC are greater than А BE , EC : Again , because the two sides CE , ED of the triangle CED are greater than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been

... AC are greater than А BE , EC : Again , because the two sides CE , ED of the triangle CED are greater than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been

**shown**that BA , AC are ... Side 22

than the base EF ; but it is not ; therefore E the angle BAC is not less than B the angle EDF ; and it was

than the base EF ; but it is not ; therefore E the angle BAC is not less than B the angle EDF ; and it was

**shown**that it is not equal to it ; therefore the angle Bac is greater than the angle EDF . Wherefore if two triangles , & c . Side 26

to the angle GKD ; and it was

to the angle GKD ; and it was

**shown**that the angle AGK is equal to the angle GhF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore A B is parallel ( 1. 27. ) to CD . ' Wherefore straight lines , & c .### 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 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.