## 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

whence A E and c are each of them equal to AV ;

equal to c ( Ax . 1 . ) , and from AB , the greater of two straight lines , a part A E

has been cut off equal to c the less . Which was to be done . PROP . IV .

whence A E and c are each of them equal to AV ;

**wherefore**the straight line AE isequal to c ( Ax . 1 . ) , and from AB , the greater of two straight lines , a part A E

has been cut off equal to c the less . Which was to be done . PROP . IV .

Side 42

also to Gk , and co to BK ;

likewise rectangular ; for cg is parallel to BK , and CB meets them ; the angles

KBC , GCB are therefore equal to two right angles ; D and KBC is a right angle ...

also to Gk , and co to BK ;

**wherefore**the H K figure CGKB is equilateral : It islikewise rectangular ; for cg is parallel to BK , and CB meets them ; the angles

KBC , GCB are therefore equal to two right angles ; D and KBC is a right angle ...

Side 48

to the alternate angle DCE ; therefore the remaining angle Dgb is half a right

angle , and is therefore equal to the angle DBG ;

equal ( 1. 6. ) to the side DG : Again , because EGF is half a right angle , and that

the E ...

to the alternate angle DCE ; therefore the remaining angle Dgb is half a right

angle , and is therefore equal to the angle DBG ;

**wherefore**also the side BD isequal ( 1. 6. ) to the side DG : Again , because EGF is half a right angle , and that

the E ...

Side 56

DB is therefore greater than DE : But DB is equal to DF ;

than DE , the less than the greater , which is impossible : Therefore the straight

line drawn from A to B does not fall without the circle . In the same manner it may

...

DB is therefore greater than DE : But DB is equal to DF ;

**wherefore**DF is greaterthan DE , the less than the greater , which is impossible : Therefore the straight

line drawn from A to B does not fall without the circle . In the same manner it may

...

Side 57

F the centre of the circle , and join EF : and because F E , a straight A line through

the centre , bisects another AC which does not pass through the centre , it shall

cut it at right ( 111. 3. ) angles ;

F the centre of the circle , and join EF : and because F E , a straight A line through

the centre , bisects another AC which does not pass through the centre , it shall

cut it at right ( 111. 3. ) angles ;

**wherefore**FEA is a right angle : Again , because ...### 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 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.