## Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ... |

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Side 51

And the straight line which stands on the other is called a

is also said to be at right angles to it. XXXVIII. An angle greater than a right angle,

/ is called obtuse. XXXIX. An angle less than a right angle, is called s acute. XL.

And the straight line which stands on the other is called a

**perpendicular**to it; andis also said to be at right angles to it. XXXVIII. An angle greater than a right angle,

/ is called obtuse. XXXIX. An angle less than a right angle, is called s acute. XL.

Side 52

XLVIII. A triangle which has a right angle, is called right-angled. The side

opposite to the right angle is called the hypotenuse. The other two sides are

sometimes called the base and

obtuse angle, ...

XLVIII. A triangle which has a right angle, is called right-angled. The side

opposite to the right angle is called the hypotenuse. The other two sides are

sometimes called the base and

**perpendicular**. XLIX. A triangle which has anobtuse angle, ...

Side 68

Second Case; if the angle BAC is equal to the sum of two right angles, BAC will

bef in one and the same straight line, and DE be bisected by the point A, and AF

be

Second Case; if the angle BAC is equal to the sum of two right angles, BAC will

bef in one and the same straight line, and DE be bisected by the point A, and AF

be

**perpendicular**to BAC and bisect the angle BAC by dividing it into two right ... Side 75

... of the other respectively. And because the several triangles are equal

respectively, the sums, which are the rectilinear figures, are equal. See Note.

PROPOSITION XXIII. PROBLEM.–To dran a straight line

PROP. xxii.

... of the other respectively. And because the several triangles are equal

respectively, the sums, which are the rectilinear figures, are equal. See Note.

PROPOSITION XXIII. PROBLEM.–To dran a straight line

**perpendicular**BOOK I.-PROP. xxii.

Side 76

To dran a straight line

length, from an assigned point nvithout it. Let AB be the assigned straight line,

which may be prolonged to any length that is desired, c both ways; and let C be

the ...

To dran a straight line

**perpendicular**to an assigned straight line of unlimitedlength, from an assigned point nvithout it. Let AB be the assigned straight line,

which may be prolonged to any length that is desired, c both ways; and let C be

the ...

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Geometry Without Axioms Or the First Book Euclid's Elements: With ... Uten tilgangsbegrensning - 1833 |

Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points aret equal assigned point axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively Scholium self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.–If third side triangle ABC tryo turned unlimited length Wherefore willf

### Populære avsnitt

Side 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...

Side 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Side 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.

Side 72 - Any two sides of a triangle are together greater than the third side.

Side 55 - 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.

Side 70 - Any two angles of a triangle are together less than two right angles.

Side 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.

Side 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.