## 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 |

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Resultat 1-5 av 35

Side 6

Things which are

which are halves of the same thing are equal to one another . 8 . Magnitudes

which coincide with one another , that is , which exactly fill the same space , are ...

Things which are

**double**of the same thing are equal to one another . 7 . Thingswhich are halves of the same thing are equal to one another . 8 . Magnitudes

which coincide with one another , that is , which exactly fill the same space , are ...

Side 39

If the sides AD , DF of A _ _ D the parallelograms ABCD , DBCF , opposite to the

base BC , be terminated at the same point D , it is plain that each of the

parallelograms is

equal to one ...

If the sides AD , DF of A _ _ D the parallelograms ABCD , DBCF , opposite to the

base BC , be terminated at the same point D , it is plain that each of the

parallelograms is

**double**of the triangle BDC ; [ I . 34 . and they are thereforeequal to one ...

Side 43

If a parallelogram and a triangle be on the same base and between the same

parallels , the parallelogram shall be

parallelogram ABCD and the triangle EBC be on the same base BC , and

between the same ...

If a parallelogram and a triangle be on the same base and between the same

parallels , the parallelogram shall be

**double**of the triangle . Let theparallelogram ABCD and the triangle EBC be on the same base BC , and

between the same ...

Side 44

... triangle ABE is equal to the triangle AEC , because they are on equal bases BE

, EC , and between the same parallels BC , AG . [ I . 38 . Therefore the triangle

ABC is

...

... triangle ABE is equal to the triangle AEC , because they are on equal bases BE

, EC , and between the same parallels BC , AG . [ I . 38 . Therefore the triangle

ABC is

**double**of the triangle A EC . But the parallelogram FECG is also**double**of...

Side 50

... sides FB , BC , each to each ; [ Definition 30 . and the angle DBA is equal to the

angle FBC ; therefore the triangle ABD is equal to the triangle FBO . [ I . 4 . Now

the parallelogram BL is

... sides FB , BC , each to each ; [ Definition 30 . and the angle DBA is equal to the

angle FBC ; therefore the triangle ABD is equal to the triangle FBO . [ I . 4 . Now

the parallelogram BL is

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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 draw 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 middle point multiple namely opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals 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 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.