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 Seiten |
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Seite 4
... sides equal : 26 . A scalene triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the ...
... sides equal : 26 . A scalene triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the ...
Seite 5
... opposite sides equal to one another , but all its sides are not equal , nor its angles right angles : 34. All other four - sided figures besides these are called trapeziums . 35. Parallel straight lines are such as are in the same plane ...
... opposite sides equal to one another , but all its sides are not equal , nor its angles right angles : 34. All other four - sided figures besides these are called trapeziums . 35. Parallel straight lines are such as are in the same plane ...
Seite 9
... sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF , and the angle BAC equal to the angle EDF : the base BC shall be ...
... sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF , and the angle BAC equal to the angle EDF : the base BC shall be ...
Seite 11
... sides are opposite , B C namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hypothesis . the remainder BF is ...
... sides are opposite , B C namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hypothesis . the remainder BF is ...
Seite 19
... opposite sides of it , make the adjacent angles toge- ther equal to two right angles , these two straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD ...
... opposite sides of it , make the adjacent angles toge- ther equal to two right angles , these two straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD ...
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Häufige Begriffe und Wortgruppen
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
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Seite 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.
Seite 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.
Seite 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Seite 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.
Seite 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.
Seite 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite 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.
Seite 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
Seite 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.
Seite 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.