## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ... |

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Side 24

All the interior angles of any

twice as many right angles as the figure has sides . For , about a point within the

figure , as many triangles may be formed as the figure has sides , each of whose

...

All the interior angles of any

**rectilineal figure**and four right angles , are equal totwice as many right angles as the figure has sides . For , about a point within the

figure , as many triangles may be formed as the figure has sides , each of whose

...

Side 29

M B Н " A D 45 P. To describe a parallelogram equal to a given

ABCD ) , having an angle equal to a given rectilineal angle ( P ) ; and to apply the

parallelogram to a given straight line ( CM ) . FI DE ( 6 ) P Produce the side CB ...

M B Н " A D 45 P. To describe a parallelogram equal to a given

**rectilineal figure**(ABCD ) , having an angle equal to a given rectilineal angle ( P ) ; and to apply the

parallelogram to a given straight line ( CM ) . FI DE ( 6 ) P Produce the side CB ...

Side 60

One

former are upon the sides of the latter . Note . — Regular polygons , which have

the same number of equal sides , thus inscribed , form a series , and have a ...

One

**rectilineal figure**is said to be inscribed in another , when all the angles of theformer are upon the sides of the latter . Note . — Regular polygons , which have

the same number of equal sides , thus inscribed , form a series , and have a ...

Side 99

Dennis M'Curdy. 22 Th . If four straight lines be proportionals , the similar

shall ...

Dennis M'Curdy. 22 Th . If four straight lines be proportionals , the similar

**rectilineal figures**described upon them shall be proportionals : and if the similar**rectilineal figures**described upon four straight lines be proportionals , those linesshall ...

Side 101

E B F P T 25 P. To describe a

equal to another given

DE : it is required to describe a

E B F P T 25 P. To describe a

**rectilineal figure**which shall be similar to one andequal to another given

**rectilineal figure**. Given the**rectilineal figures**ABC andDE : it is required to describe a

**rectilineal figure**similar to ABC , and equal to DE .### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... Dennis M'Curdy Uten tilgangsbegrensning - 1846 |

Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |

Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

ABCD alternate antecedents applied Argument base bisected centre Chart chord circle circle ABC circumference common consequents Constr contained described diameter difference divided draw drawn equal angles equiangular equilateral equimultiples exceeds excess exterior extreme fore four fourth Geometry given given straight line gles greater half Hence inscribed interior join less magnitudes mean measure meet multiple namely opposite parallel parallelogram pass perpendicular plane polygon produced proportionals propositions proved Q. E. D. Recite radius ratio rectangle rectilineal figure remainders right angles School segment sides similar sine solid square straight line taken tangent third touch triangle ABC unequal Wherefore whole

### Populære avsnitt

Side 90 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

Side 117 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Side 92 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Side 79 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.

Side 87 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally...

Side 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Side 133 - If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.

Side 13 - AB be the greater, and from it cut (3. 1.) off DB equal to AC the less, and join DC ; therefore, because A in the triangles DBC, ACB, DB is equal to AC, and BC common to both, the two sides DB, BC are equal to the two AC, CB. each to each ; and the angle DBC is equal to the angle ACB; therefore the base DC is equal to the base AB, and the triangle DBC is< equal to the triangle (4. 1.) ACB, the less to 'the greater; which is absurd.

Side 71 - If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall...

Side 83 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words