## 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

AB to DE , and AC A to df ; and the angle BAC equal to the angle EDF , the base

BC shall be equal to the base EF ; and the

the other der B E T angles , to which the equal sides are opposite , shall be ...

AB to DE , and AC A to df ; and the angle BAC equal to the angle EDF , the base

BC shall be equal to the base EF ; and the

**triangle ABC**to the triangle DEF ; andthe other der B E T angles , to which the equal sides are opposite , shall be ...

Side 15

to the three angles CBA , A BE , EBD . Again , because the angle DBA is equal to

the two angles DBE , EBA , add to these equals the

angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles

...

to the three angles CBA , A BE , EBD . Again , because the angle DBA is equal to

the two angles DBE , EBA , add to these equals the

**angle ABC**; therefore theangles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles

...

Side 17

the

bisected , it may be demonstrated that the

to D ; and because ACD is the exterior

greater ( 1.

the

**angle**ACD is greater than B A E. In the same manner , if the side bc bebisected , it may be demonstrated that the

**angle**BCG , that is ( 1. ... Produce BCto D ; and because ACD is the exterior

**angle**of the**triangle**B**ABC**, ACD isgreater ( 1.

Side 71

to two right angles , the three angles of the triangle CA B , viz . the angles CA B ,

ABC , BCA , are equal to two right angles ... to the angle CDB , because they are

in the same segment BADC , D and the

to two right angles , the three angles of the triangle CA B , viz . the angles CA B ,

ABC , BCA , are equal to two right angles ... to the angle CDB , because they are

in the same segment BADC , D and the

**angle ACB**is equal to the angle ADB ... Side 77

F In a circle , the angle in a semicircle is a right angle ; but the angle in a segment

greater than a semicircle is less than a ... to the two

the angle BAC is equal to the angle FAC , and each of them is therefore a right ...

F In a circle , the angle in a semicircle is a right angle ; but the angle in a segment

greater than a semicircle is less than a ... to the two

**angles ABC**, ACB ; thereforethe angle BAC is equal to the angle FAC , and each of them is therefore a right ...

### 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.