## 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 39

In every parallelogram , any of the parallelograms about a diameter , together

with the two A E D complements , is called a

Hg , together with the complements AF , FC , H K is the

с ...

In every parallelogram , any of the parallelograms about a diameter , together

with the two A E D complements , is called a

**Gnomon**. “ Thus the parallelogramHg , together with the complements AF , FC , H K is the

**gnomon**, which is more Bс ...

Side 43

to DB ; and DF , together with ch , is the

Cmg is equal to the rectangle AD , DB : To each of these add LG , which is equal

( 11. 4. Cor . ) to the square of CD , therefore the

is ...

to DB ; and DF , together with ch , is the

**gnomon**CMG ; therefore the**gnomon**Cmg is equal to the rectangle AD , DB : To each of these add LG , which is equal

( 11. 4. Cor . ) to the square of CD , therefore the

**gnomon**GMG , together with lg ,is ...

Side 44

to DB : Therefore the

each of these LG , which is equal to the ... DB , together with the square of CB , is

equal to the

up ...

to DB : Therefore the

**gnomon**CMG is equal to the rectangle AD , DB : Add toeach of these LG , which is equal to the ... DB , together with the square of CB , is

equal to the

**gnomon**CMG and the figure LG : But the**gnomon**cug and LG makeup ...

Side 45

... PL , RF are equal to one another , and so are quadruple of one of them AG ;

and it was demonstrated , that the four CK , BN , GR , and in are quadruple of ck :

Therefore the eight rectangles which contain the

...

... PL , RF are equal to one another , and so are quadruple of one of them AG ;

and it was demonstrated , that the four CK , BN , GR , and in are quadruple of ck :

Therefore the eight rectangles which contain the

**gnomon**AOH , are quadruple of...

Side 46

to the square of Ac ; Therefore four times the rectangle AB , BC , together with the

square of a c , is equal to the

AOH and xh make up the figure AEFD , which is the square of AD : Therefore four

...

to the square of Ac ; Therefore four times the rectangle AB , BC , together with the

square of a c , is equal to the

**gnomon**Aon and the square xh : But the**gnomon**AOH and xh make up the figure AEFD , which is the square of AD : Therefore four

...

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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 to FB equilateral exterior angle extremity figure fore four given point given straight line greater half impossible interior isosceles triangle join less Let ABC Let the straight likewise 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 side bc sides squares of AC straight lines 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.