A Text-book of Euclid's Elements for the Use of Schools, Βιβλίο 1Macmillan, 1904 - 456 σελίδες |
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Σελίδα 1
... plane surface is frequently referred to simply as a plane . NOTE . Euclid regards a point merely as a mark of position , and he therefore attaches to it no idea of size and shape . Similarly he considers that the properties of a line ...
... plane surface is frequently referred to simply as a plane . NOTE . Euclid regards a point merely as a mark of position , and he therefore attaches to it no idea of size and shape . Similarly he considers that the properties of a line ...
Σελίδα 2
... plane rectilineal angle is the inclina- tion of two straight lines to one another , which meet together , but are not in the same straight line . See Def . 9. ] The point at which the straight lines meet is called the vertex of the ...
... plane rectilineal angle is the inclina- tion of two straight lines to one another , which meet together , but are not in the same straight line . See Def . 9. ] The point at which the straight lines meet is called the vertex of the ...
Σελίδα 4
... plane surface bounded by one or more lines is called a plane figure . The sum of the bounding lines is called the perimeter of the figure . Two figures are said to be equal in area when they enclose equal 3 portions of a plane surface ...
... plane surface bounded by one or more lines is called a plane figure . The sum of the bounding lines is called the perimeter of the figure . Two figures are said to be equal in area when they enclose equal 3 portions of a plane surface ...
Σελίδα 5
Euclid. 22. A quadrilateral is a plane figure bounded by four straight lines . The straight line which joins opposite angular points in a quadrilateral is called a diagonal . 23. A polygon is a plane figure bounded by more than four ...
Euclid. 22. A quadrilateral is a plane figure bounded by four straight lines . The straight line which joins opposite angular points in a quadrilateral is called a diagonal . 23. A polygon is a plane figure bounded by more than four ...
Σελίδα 6
... plane , do not meet , how- ever far they are produced in either direc- tion . 36. A Parallelogram is a four - sided figure which has its opposite sides parallel . 37. A rectangle is a parallelogram which has one of its angles a right ...
... plane , do not meet , how- ever far they are produced in either direc- tion . 36. A Parallelogram is a four - sided figure which has its opposite sides parallel . 37. A rectangle is a parallelogram which has one of its angles a right ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 340 - 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.
Σελίδα 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Σελίδα 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Σελίδα 162 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Σελίδα 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 18 - 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 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.