Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes; a Series of Questions on Each Book; and a Selection of Geometrical Exercises from the Senate-house and College Examination Papers, with Hints, &c. Designed for the Use of the Junior Classes in Public and Private Schools. the first six books, and the portions of the eleventh and twelfth books read at CambridgeLongman, Green, Longman, Roberts, and Green, 1868 - 410 Seiten |
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Seite 83
... segments of the base . 150. If from the middle point of one of the sides of a right - angled triangle , a perpendicular be drawn to the hypotenuse , the difference of the squares on the segments into which it is divided , is equal to ...
... segments of the base . 150. If from the middle point of one of the sides of a right - angled triangle , a perpendicular be drawn to the hypotenuse , the difference of the squares on the segments into which it is divided , is equal to ...
Seite 104
... segments of the line , according as the point of section is in the line or the line produced . Prop . vi . Algebraically . Let AB contain 2a linear units , then its half BC contains a units ; and let BD contain m units . Then AD ...
... segments of the line , according as the point of section is in the line or the line produced . Prop . vi . Algebraically . Let AB contain 2a linear units , then its half BC contains a units ; and let BD contain m units . Then AD ...
Seite 106
... = CA ' , Hence CF is divided in , in the same manner as AB is divided in H , by adding AF a line equal to the greater segment , to the given line CA or AB . And by successively adding to the last 106 EUCLID'S ELEMENTS .
... = CA ' , Hence CF is divided in , in the same manner as AB is divided in H , by adding AF a line equal to the greater segment , to the given line CA or AB . And by successively adding to the last 106 EUCLID'S ELEMENTS .
Seite 107
... segment , a series of lines increasing in magnitude may be found similarly divided to AB . It may also be shewn that the squares on the whole line and on the less segment are equal to three times the square on the greater segment ...
... segment , a series of lines increasing in magnitude may be found similarly divided to AB . It may also be shewn that the squares on the whole line and on the less segment are equal to three times the square on the greater segment ...
Seite 111
... segments of a line or the difference of the internal segments is double the distance between the points of section and bisection of the line . 26. Shew how Euc . 11. 6 , may be deduced immediately from the preceding Proposition . 27 ...
... segments of a line or the difference of the internal segments is double the distance between the points of section and bisection of the line . 26. Shew how Euc . 11. 6 , may be deduced immediately from the preceding Proposition . 27 ...
Häufige Begriffe und Wortgruppen
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc base BC chord circle ABC constr demonstrated describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane polygon problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral figure radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Beliebte Passagen
Seite 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Seite 2 - 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 317 - 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 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Seite 88 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 9 - 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 22 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other...
Seite 92 - 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...