## 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 1-5 av 51

Side 255

Thus , in the manner of I . 4 , we can

angle ACB . I . 6 is the converse of part of I . 5 . One proposition is said to be the

converse of another when the conclusion of each is the hypothesis of the other .

Thus , in the manner of I . 4 , we can

**shew**that the angle ABC is equal to theangle ACB . I . 6 is the converse of part of I . 5 . One proposition is said to be the

converse of another when the conclusion of each is the hypothesis of the other .

Side 260

Or we may

of DF and EG . Then , the angle DHG is greater than the angle DEG , by I . 16 ;

the angle DEG is not less than the angle DGE , by I . 18 ; therefore the angle DHG

...

Or we may

**shew**it in the following manner . Let H denote the point of intersectionof DF and EG . Then , the angle DHG is greater than the angle DEG , by I . 16 ;

the angle DEG is not less than the angle DGE , by I . 18 ; therefore the angle DHG

...

Side 263

Here we may in the same way

to CD , they are parallel to each other . It has been said that the case considered

in the text is 80 obvious as to need no demonstration ; for if AB and CD can never

...

Here we may in the same way

**shew**that if A B and EP are each of them parallelto CD , they are parallel to each other . It has been said that the case considered

in the text is 80 obvious as to need no demonstration ; for if AB and CD can never

...

Side 269

... they are of great importance in Trigonometry ; they are however not required in

any of the parts of Euclid ' s Elements which are usually read . The converse of I .

47 is proved in I . 48 ; and we can easily

... they are of great importance in Trigonometry ; they are however not required in

any of the parts of Euclid ' s Elements which are usually read . The converse of I .

47 is proved in I . 48 ; and we can easily

**shew**that converses of II . 12 and II . Side 274

Thus , in order to

the second supposed point of contact on the direction of the straight line which

joins the centres . Accordingly in his own demonstration Euclid confines himself ...

Thus , in order to

**shew**that there is only one point of contact , it is sufficient to putthe second supposed point of contact on the direction of the straight line which

joins the centres . Accordingly in his own demonstration Euclid confines himself ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.