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 σελίδες |
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Σελίδα
... means of developing and cultivating the reason : and that " the object of a liberal education is to develope the whole mental system of man ; -to make his speculative inferences coincide with his practical convictions ; -to enable him ...
... means of developing and cultivating the reason : and that " the object of a liberal education is to develope the whole mental system of man ; -to make his speculative inferences coincide with his practical convictions ; -to enable him ...
Σελίδα 42
... means , a visible sign or mark on a surface , in other words , a physical point . The English term point , means the sharp end of any thing , or a mark made by it . The word point comes from the Latin punctum , through the French word ...
... means , a visible sign or mark on a surface , in other words , a physical point . The English term point , means the sharp end of any thing , or a mark made by it . The word point comes from the Latin punctum , through the French word ...
Σελίδα 43
... mean , that no part of the line which is called a straight line deviates either from one side or the other of the direction which is fixed by the extremities of the line ; and thus it may be distinguished from a curved line , which does ...
... mean , that no part of the line which is called a straight line deviates either from one side or the other of the direction which is fixed by the extremities of the line ; and thus it may be distinguished from a curved line , which does ...
Σελίδα 49
... means of self - evident axioms , or of propositions already demonstrated . 8. To substitute mentally the definition instead of the thing defined . " Of these rules , he says , " the first , fourth and sixth are not absolutely necessary ...
... means of self - evident axioms , or of propositions already demonstrated . 8. To substitute mentally the definition instead of the thing defined . " Of these rules , he says , " the first , fourth and sixth are not absolutely necessary ...
Σελίδα 50
... means of syllogisms founded on the axioms and definitions . Every syllogism consists of three propositions , of which , two are called the premisses , and the third , the conclusion . These propositions contain three terms , the subject ...
... means of syllogisms founded on the axioms and definitions . Every syllogism consists of three propositions , of which , two are called the premisses , and the third , the conclusion . These propositions contain three terms , the subject ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...