## 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 9

angles contained by those sides equal to one another , their bases shall likewise

be equal , and the triangles be equal ... B to the

each to each , to which the equal sides are opposite ; viz . the angle ACF to the ...

angles contained by those sides equal to one another , their bases shall likewise

be equal , and the triangles be equal ... B to the

**remaining angles**of the other ,each to each , to which the equal sides are opposite ; viz . the angle ACF to the ...

Side 16

to two right angles ; and CEA , A ED have been demonstrated to be equal to two

right angles ; wherefore the angles CEA , AED are equal to the angles A ED , DE

B. Take away the common angle AED , and the

to two right angles ; and CEA , A ED have been demonstrated to be equal to two

right angles ; wherefore the angles CEA , AED are equal to the angles A ED , DE

B. Take away the common angle AED , and the

**remaining angle**CEA is equal ... Side 46

to the interior and opposite angle ECB , the

angle ; therefore , the angle GEF is equal to the angle EFG , and the side Eg

equal ( 1.6 . ) to the side GF : Again , because the angle at B is half a right angle

and ...

to the interior and opposite angle ECB , the

**remaining angle**EFG is half a rightangle ; therefore , the angle GEF is equal to the angle EFG , and the side Eg

equal ( 1.6 . ) to the side GF : Again , because the angle at B is half a right angle

and ...

Side 48

B G angle EAC ; and the angle ACE is a right angle ; therefore each of the angles

CEA , EAC is half a right angle ( 1. 32. ) ... to the alternate angle DCE ; therefore

the

...

B G angle EAC ; and the angle ACE is a right angle ; therefore each of the angles

CEA , EAC is half a right angle ( 1. 32. ) ... to the alternate angle DCE ; therefore

the

**remaining angle**DGB is half a right angle , and is therefore equal to the angle...

Side 78

to a right angle : But ABF is likewise a right angle ; there . E fore the angle ABF is

equal to the angles BAD , ABD : Take from these equals the common angle ABD ;

therefore the

to a right angle : But ABF is likewise a right angle ; there . E fore the angle ABF is

equal to the angles BAD , ABD : Take from these equals the common angle ABD ;

therefore the

**remaining angle**DBF is equal to the angle BAD , which is in the ...### 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 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.