## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |

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Resultat 1-5 av 5

Side 71

to the angle CDB , because they are in the same

angle ACB is equal to the angle ADB , because they are in the same

ADCB : Therefore the whole angle ADC is equal to the angles CA B , ACB : To

each of ...

to the angle CDB , because they are in the same

**segment**BADC , D and theangle ACB is equal to the angle ADB , because they are in the same

**segment**ADCB : Therefore the whole angle ADC is equal to the angles CA B , ACB : To

each of ...

Side 72

Therefore , there cannot be two similar

of the same line , which do not coincide . ... Let A E B , CFD be similar

of circles upon the equal straight lines AB , CD ; the

...

Therefore , there cannot be two similar

**segments**of a circle upon the same sideof the same line , which do not coincide . ... Let A E B , CFD be similar

**segments**of circles upon the equal straight lines AB , CD ; the

**segment**A EB is equal to the...

Side 77

F In a circle , the angle in a semicircle is a right angle ; but the angle in a

greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw ca dividing the circle into the

F In a circle , the angle in a semicircle is a right angle ; but the angle in a

**segment**greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw ca dividing the circle into the

**segments**... Side 78

greater

to be less , than a right angle . ... made by this line with the line touching the circle

, shall be equal to the angles which are in the alternate

greater

**segment**is said to be greater , and the angle of the less**segment**is saidto be less , than a right angle . ... made by this line with the line touching the circle

, shall be equal to the angles which are in the alternate

**segments**of the circle . Side 80

To cut off a

given rectilineal angle . Let ABC be the given circle , and d the given rectilineal

angle ; it is required to cut off a

...

To cut off a

**segment**from a given circle which shall contain an angle equal to agiven rectilineal angle . Let ABC be the given circle , and d the given rectilineal

angle ; it is required to cut off a

**segment**from the circle ABC that shall contain an...

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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.