## 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

If two triangles have two

each ; and have likewise the angles contained by those

another ; they shall likewise have their bases , or third

...

If two triangles have two

**sides**of the one equal to two**sides**of the other , each toeach ; and have likewise the angles contained by those

**sides**equal to oneanother ; they shall likewise have their bases , or third

**sides**, equal ; and the two...

Side 11

The case in which the vertex of the triangle is upon a

demonstration . Therefore , upon the same base , and on the same

there cannot be two triangles , that have their

The case in which the vertex of the triangle is upon a

**side**of the other , needs nodemonstration . Therefore , upon the same base , and on the same

**sides**of it ,there cannot be two triangles , that have their

**sides**which are terminated in one ... Side 18

The greater angle of every triangle is subtended by the greater

greater

greater than the angle BCA ; the

, if it ...

The greater angle of every triangle is subtended by the greater

**side**, or has thegreater

**side**opposite to it . Let ABC be a triangle , of which the angle ABC isgreater than the angle BCA ; the

**side**ac is likewise greater than the**side**A B. For, if it ...

Side 21

If two triangles have two

each , but the angle contained by the two

angle contained by the two

If two triangles have two

**sides**of the one equal to two**sides**of the other , each toeach , but the angle contained by the two

**sides**of one of them greater than theangle contained by the two

**sides**equal to them , of the other ; the base of that ... Side 89

ACBH be a trapezium , whose

the adjacent points be joined ; then the figure DEGF is a parallelogram . Draw the

diagonals AB , CH . Since AC , BC are bisected in D and E ( Theorem 1. No. 1. ) ...

ACBH be a trapezium , whose

**sides**are bisected in the points D , E , G and F ; letthe adjacent points be joined ; then the figure DEGF is a parallelogram . Draw the

diagonals AB , CH . Since AC , BC are bisected in D and E ( Theorem 1. No. 1. ) ...

### 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.