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 ExercisesMacmillan, 1883 - 400 sider |
Inni boken
Resultat 6-10 av 60
Side 71
... , when the perpendicu- lars drawn to them from the centre are equal . 5. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . 6. A segment of a circle is the figure contained Book III.
... , when the perpendicu- lars drawn to them from the centre are equal . 5. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . 6. A segment of a circle is the figure contained Book III.
Side 89
... perpendicular to AF ; FE [ I. 12 . H let DG meet the circumference at H. Then , because the angle DGA is a right angle , [ Construction . B the angle DAG is less than a right angle ; [ I. 17 . therefore DA is greater than DG . [ I.19 ...
... perpendicular to AF ; FE [ I. 12 . H let DG meet the circumference at H. Then , because the angle DGA is a right angle , [ Construction . B the angle DAG is less than a right angle ; [ I. 17 . therefore DA is greater than DG . [ I.19 ...
Side 91
... perpendicular to DE . For if not , let FG be drawn from the point F perpen- dicular to DE , meeting the cir ... perpendicular to DE . In the same manner it may be shewn that no other straight line from F is perpendicular to DE , but FC ...
... perpendicular to DE . For if not , let FG be drawn from the point F perpen- dicular to DE , meeting the cir ... perpendicular to DE . In the same manner it may be shewn that no other straight line from F is perpendicular to DE , but FC ...
Side 92
... perpendicular to DE ; [ III . 18 . thereforethe angle FCEis a right angle . But the angle ACE is also a right angle ; [ Construction . E therefore the angle FCE is equal to the angle ACE , [ Ax . 11 . the less to the greater ; which is ...
... perpendicular to DE ; [ III . 18 . thereforethe angle FCEis a right angle . But the angle ACE is also a right angle ; [ Construction . E therefore the angle FCE is equal to the angle ACE , [ Ax . 11 . the less to the greater ; which is ...
Side 108
... point E , but not at right angles . Then , if BD be bisected at F , F is the centre of the circle ABCD ; join AF , and from F draw FG perpendicular to AC . [ I. 12 . Then AG is equal to GC ; [ III . 108 EUCLID'S ELEMENTS .
... point E , but not at right angles . Then , if BD be bisected at F , F is the centre of the circle ABCD ; join AF , and from F draw FG perpendicular to AC . [ I. 12 . Then AG is equal to GC ; [ III . 108 EUCLID'S ELEMENTS .
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: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1884 |
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 ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Populære avsnitt
Side 262 - 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 71 - 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 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Side 182 - 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 8 - 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 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 58 - 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 60 - 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 242 - 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 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.