The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 sider |
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Resultat 1-5 av 52
Side 189
... and being produced does not cut it . Such a straight line is called a tangent to the circle . A straight line which cuts a circle is called a secant . PROPOSITION 16. THEOREM . The straight line drawn at right Book III . Prop . 15 . 189.
... and being produced does not cut it . Such a straight line is called a tangent to the circle . A straight line which cuts a circle is called a secant . PROPOSITION 16. THEOREM . The straight line drawn at right Book III . Prop . 15 . 189.
Side 191
... tangents to a curve it is said that the lines envelop that curve , and the curve is said to be the envelope of the set . Thus we have shown in III . 16 ( 1 ) that The straight lines equidistant from a fixed point envelop a circle which ...
... tangents to a curve it is said that the lines envelop that curve , and the curve is said to be the envelope of the set . Thus we have shown in III . 16 ( 1 ) that The straight lines equidistant from a fixed point envelop a circle which ...
Side 192
... tangent to PQR from O. PQR ; it is required Find the centre C of PQR . Join OC , and bisect OC in E ; with centre E and distance EC or EO describe a ting PQR in P. PQR . Produce OP to F. cut- Join OP . OP shall be a tangent to R F EP EO ...
... tangent to PQR from O. PQR ; it is required Find the centre C of PQR . Join OC , and bisect OC in E ; with centre E and distance EC or EO describe a ting PQR in P. PQR . Produce OP to F. cut- Join OP . OP shall be a tangent to R F EP EO ...
Side 193
... tangent to PQR . We have therefore demonstrated that From an external point O two tangents can be drawn to a given circle . 2. The two tangents OP , OQ which can be drawn from an ex- ternal point O to a given circle are equal . In the ...
... tangent to PQR . We have therefore demonstrated that From an external point O two tangents can be drawn to a given circle . 2. The two tangents OP , OQ which can be drawn from an ex- ternal point O to a given circle are equal . In the ...
Side 194
... tangents to the described with centre O , and radius OP or OQ . When two intersecting circles , as in this exercise ... tangent to two given circles . Q A R C A D R required is the centres of the two Os AQF , BRG , A and B the the Oces ...
... tangents to the described with centre O , and radius OP or OQ . When two intersecting circles , as in this exercise ... tangent to two given circles . Q A R C A D R required is the centres of the two Os AQF , BRG , A and B the the Oces ...
Andre utgaver - Vis alle
The Harper Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Euclid,Edward Mann Langley,W. Seys Phillips Uten tilgangsbegrensning - 1890 |
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Euclid,Edward Mann Langley,W. Seys Phillips Uten tilgangsbegrensning - 1894 |
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices
Populære avsnitt
Side 21 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 369 - 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.
Side 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Side 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Side 96 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 40 - Any two sides of a triangle are together greater than the third side.
Side 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Side 407 - 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.
Side 156 - 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...