## The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises |

### Inni boken

Resultat 16-20 av 60

Side 45

Axiom 3 . Wherefore , the complements & c . Q . E . D . PROPOSITION 44 .

equal to a given triangle , and have one of its angles equal to a given rectilineal

angle .

Axiom 3 . Wherefore , the complements & c . Q . E . D . PROPOSITION 44 .

**PROBLEM**. To a given straight line to apply a parallelogram , which shall beequal to a given triangle , and have one of its angles equal to a given rectilineal

angle .

Side 47

having an angle equal to a given rectilineal angle . Let ABCD be the given

rectilineal figure , and E the given rectilineal angle : it is required to describe a ...

**PROBLEM**. To describe a parallelogram equal to a given rectilineal figure , andhaving an angle equal to a given rectilineal angle . Let ABCD be the given

rectilineal figure , and E the given rectilineal angle : it is required to describe a ...

Side 48

... and shall be equal to a given rectilineal figure ; namely , by applying to the

given straight line a parallelogram equal to the first triangłe ABD , and having an

angle equal to the given angle ; and so on . [ I . 44 . PROPOSITION 46 .

... and shall be equal to a given rectilineal figure ; namely , by applying to the

given straight line a parallelogram equal to the first triangłe ABD , and having an

angle equal to the given angle ; and so on . [ I . 44 . PROPOSITION 46 .

**PROBLEM**. Side 49

straight line : it is required to describe a square on AB . From the point A draw .

AC at right angles to AB ; [ 1 . 11 . and make AD equal to AB ; [ I . 3 . through D

draw ...

**PROBLEM**. To describe a square on a given straight line . Let AB be the givenstraight line : it is required to describe a square on AB . From the point A draw .

AC at right angles to AB ; [ 1 . 11 . and make AD equal to AB ; [ I . 3 . through D

draw ...

Side 65

... the Bquares on AC , CD . And DG is equal to DB ; therefore the squares on AD

, DB are double of the squares on AC , CD . Wherefore , if a straight line & c . Q .

E . D . PROPOSITION 11 .

.

... the Bquares on AC , CD . And DG is equal to DB ; therefore the squares on AD

, DB are double of the squares on AC , CD . Wherefore , if a straight line & c . Q .

E . D . PROPOSITION 11 .

**PROBLEM**. To divide a given straight BOOK II . 10 . 65.

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The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Isaac Todhunter Uten tilgangsbegrensning - 1880 |

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1867 |

### Vanlige uttrykk og setninger

ABCD AC is equal angle ABC angle BAC Axiom base bisected Book centre chord circle ABC circumference common Construction Corollary Definition demonstration describe a circle described diameter difference divided double drawn equal equal angles equiangular equilateral equimultiples Euclid extremities fall figure fixed formed four fourth given circle given point given straight line greater half Hypothesis inscribed intersect join less Let ABC magnitudes manner meet multiple namely opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals PROPOSITION Q.E.D. PROPOSITION quadrilateral radius ratio reason rectangle contained rectilineal figure remaining respectively right angles segment shew shewn sides similar square straight line drawn suppose Take taken tangent THEOREM third triangle ABC twice Wherefore whole

### Populære avsnitt

Side 264 - 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.

Side 73 - 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 264 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...

Side 184 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 10 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.

Side 60 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 62 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB

Side 244 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.

Side 6 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.