## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |

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Resultat 1-5 av 36

Side 2

An obtuse angle is that which is greater than a right angle . XII . An acute angle is

that which is

any thing . " XIV . A figure is that which is inclosed by 2 EUCLID'S ELEMENTS .

An obtuse angle is that which is greater than a right angle . XII . An acute angle is

that which is

**less**than a right angle . XIII . “ A term or boundary is the extremity ofany thing . " XIV . A figure is that which is inclosed by 2 EUCLID'S ELEMENTS .

Side 6

If a straight line meet two straight lines , so as to make the two interior angles on

the same side of it taken together

being continually produced , shall at length meet upon that side on which are the

...

If a straight line meet two straight lines , so as to make the two interior angles on

the same side of it taken together

**less**than two right angles , these straight linesbeing continually produced , shall at length meet upon that side on which are the

...

Side 8

Wherefore from the given point A a straight line AL has been drawn equal to the

given straight line BC . Which was to be done . PROP . III . PROBLEM . From the

greater of two given straight lines to cut off a part equal to the

...

Wherefore from the given point A a straight line AL has been drawn equal to the

given straight line BC . Which was to be done . PROP . III . PROBLEM . From the

greater of two given straight lines to cut off a part equal to the

**less**. Let AB and C...

Side 10

to AF , the

( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to

each ; and they contain the angle FAG common to the two triangles AFC , AGB ...

to AF , the

**less**, and join FC , GB . Because AF is equal ( Constr . ) to AG , and AB( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to

each ; and they contain the angle FAG common to the two triangles AFC , AGB ...

Side 11

The base DC is equal to the base AB , and the triangle DBC is equal to the

triangle ACB , the

unequal to AC ; that is , it is equal to it . Wherefore , if two angles , & c . Q.E.D ,

COR .

The base DC is equal to the base AB , and the triangle DBC is equal to the

triangle ACB , the

**less**to the greater ; which is absurd . Therefore 3 . AB is notunequal to AC ; that is , it is equal to it . Wherefore , if two angles , & c . Q.E.D ,

COR .

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The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Uten tilgangsbegrensning - 1854 |

### Vanlige uttrykk og setninger

ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base base BC bisected centre circle ABC circumference coincide common cuts the circle demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line given triangle greater impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown sides square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle wherefore whole

### Populære avsnitt

Side 26 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...

Side 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

Side 97 - 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 7 - AB; but things which are equal to the same are equal to one another...

Side 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.

Side 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.

Side 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 52 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced...