## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |

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Resultat 1-5 av 5

Side 47

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**gnomon**. A E D H F Ᏼ G C " Thus the parallelogram HG , together with the complements AF , FC , is the**gnomon**, which is more briefly expressed by the letters 4GK , or EHC , which are at the opposite angles of the parallelograms which ... Side 52

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**gnomon**CMG ; therefore 4. The**gnomon**CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( II . 4. Cor . ) to the square of CD ; therefore 5. The**gnomon**CMG , together with LG , is equal to the rectangle AD ... Side 53

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**gnomon**AKF , together with the square CK ; there- fore but 3. The**gnomon**AKF , together with the square CK , is double of AK ; 4. Twice the rectangle AB , BC , is double of AK , for BK is equal ( II . 4. Cor . ) to BC ; therefore 5. The ... Side 54

Euclides Samuel A Good. but the

Euclides Samuel A Good. but the

**gnomon**AKF , together with the squares CK , HF , make up the whole figure ADEB and CK , which are the squares of AB and BC ; therefore 7. The squares of AB and BC are equal to twice the rectangle AB , BC ... Side 55

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**gnomon**40H was demonstrated to be quadruple of AK ; there- fore 12. Four times the rectangle AB , BC , is equal to the**gnomon**AOH ; to each of these add XH , which is equal ( II . 4. Cor . ) to the square of AC ; therefore 13. Four ...### Andre utgaver - Vis alle

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

The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... EUCLID.,Samuel A. GOOD Uten tilgangsbegrensning - 1854 |

### Vanlige uttrykk og setninger

ABC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EAB angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double equal angles equal Constr equal Hyp equal straight lines equal to BC equiangular equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given rectilineal angle given straight line given triangle gnomon greater inscribed join Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F Q.E.D. PROP rectangle AD rectangle AE rectangle contained rectilineal figure remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle

### 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...