## 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 10

If two angles of a triangle be equal to one another , the sides also which subtend ,

or are opposite to , the equal angles , shall be equal to one another . Let ABC be

a triangle having the

If two angles of a triangle be equal to one another , the sides also which subtend ,

or are opposite to , the equal angles , shall be equal to one another . Let ABC be

a triangle having the

**angle ABC**equal to the**angle ACB**; the side AB is also ... Side 17

Let ABC be any triangle ; any two of A its angles together are less than two right

angles . ... than the с interior and opposite

Let ABC be any triangle ; any two of A its angles together are less than two right

angles . ... than the с interior and opposite

**angle ABC**; to each of these add the**angle ACB**; therefore the angles ACD , ACB are greater than the**angles ABC**... Side 27

Again , because AB is parallel to CE , and BD B C falls upon them , the exterior

angle Ecd is equal to the interior and opposite

was shown to be equal to the angle BAC ; therefore the whole exterior angle acp

is ...

Again , because AB is parallel to CE , and BD B C falls upon them , the exterior

angle Ecd is equal to the interior and opposite

**angle ABC**; but the angle ACEwas shown to be equal to the angle BAC ; therefore the whole exterior angle acp

is ...

Side 28

four right angles ; therefore all the exterior angles are equal to four right angles .

B PROP . XXXIII . ... Join BC ; and because AB is parallel to CD , and BC meets

them , the alternate С

...

four right angles ; therefore all the exterior angles are equal to four right angles .

B PROP . XXXIII . ... Join BC ; and because AB is parallel to CD , and BC meets

them , the alternate С

**angles ABC**, BCD are equal ( 1. 29. ) ; and because AB is...

Side 71

The opposite angles of any quadrilateral figure inscribed in a circle , are together

equal to two right angles . ... to the angle CDB , because they are in the same

segment BADC , D and the

The opposite angles of any quadrilateral figure inscribed in a circle , are together

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 , because they ...### 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.