A Text-book of Euclid's Elements for the Use of Schools, Libro 1Macmillan, 1904 - 456 páginas |
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Página 1
... extremities of a line are points , and the intersection of two lines is a point . 4. A straight line is that which lies evenly between its extreme points . Any portion cut off from a straight line is called a segment of it . 5. A ...
... extremities of a line are points , and the intersection of two lines is a point . 4. A straight line is that which lies evenly between its extreme points . Any portion cut off from a straight line is called a segment of it . 5. A ...
Página 3
... which the greater ( ii ) is said to be reflex . If the arms OA , OB are in the same straight line , the angle formed by them on either side is called a straight angle . ] B A B A 13 . A term or boundary is the extremity of DEFINITIONS . 3.
... which the greater ( ii ) is said to be reflex . If the arms OA , OB are in the same straight line , the angle formed by them on either side is called a straight angle . ] B A B A 13 . A term or boundary is the extremity of DEFINITIONS . 3.
Página 4
Euclid. 13 . A term or boundary is the extremity of anything . 14. Any portion of a 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 ...
Euclid. 13 . A term or boundary is the extremity of anything . 14. Any portion of a 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 ...
Página 15
... extremity of the line BC ; the equilateral triangle may be described on either side of the line so drawn ; and the sides of the equilateral triangle may be produced in either direction . Thus there are in general 2 × 2 × 2 , or eight ...
... extremity of the line BC ; the equilateral triangle may be described on either side of the line so drawn ; and the sides of the equilateral triangle may be produced in either direction . Thus there are in general 2 × 2 × 2 , or eight ...
Página 22
... extremity of the base equal to one another , and likewise those which are terminated at the other extremity equal to one another . A B If it be possible , on the same base AB , and on the same side of it , let there be two triangles ACB ...
... extremity of the base equal to one another , and likewise those which are terminated at the other extremity equal to one another . A B If it be possible , on the same base AB , and on the same side of it , let there be two triangles ACB ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Página 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...
Página 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 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.
Página 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.
Página 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.