## 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 46

Side 2

An obtuse angle is that which is

that which is less than a right angle . XIII . “ A term or boundary is the extremity of

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 isthat which is less than a right angle . XIII . “ A term or boundary is the extremity of

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

Side 6

The whole is

XI . All right angles are equal to one another . XII . “ If a straight line meet two

straight lines , so as to make the two interior angles on the same side of it taken ...

The whole is

**greater**than its part . X. Two straight lines cannot inclose a space .XI . All right angles are equal to one another . XII . “ If a straight line meet two

straight lines , so as to make the two interior angles on the same side of it taken ...

Side 8

Which was to be done . PROP . III . PROBLEM . From the

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

Which was to be done . PROP . III . PROBLEM . From the

**greater**of two givenstraight 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**. It is required to cut off from AB , the**greater**, a ... Side 10

А B В F G D E In BD take any point F , and from AE , the

( I. 3. ) 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 ...

А B В F G D E In BD take any point F , and from AE , the

**greater**, cut off AG equal( I. 3. ) 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 ...

Side 11

A D B For if AB be not equal to AC , one of them is

be the

Therefore because in the triangles DBC , ACB , DB is equal to AC , and BC ...

A D B For if AB be not equal to AC , one of them is

**greater**than the other . Let ABbe the

**greater**, and from it cut off ( I. 3. ) DB equal to AC , the less , and join DČ .Therefore because in the triangles DBC , ACB , DB is equal to AC , and BC ...

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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...