Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations in Euclid, part ii., with illustr. [&c.] by H. Green1861 |
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Página 35
... constructed an instrument of this kind . Its general nature may be seen from the following representation , in which the approach of the chord BF to the diam . NS may be measured , either by the perp . CD , or the arc BQ . Let NESQ be a ...
... constructed an instrument of this kind . Its general nature may be seen from the following representation , in which the approach of the chord BF to the diam . NS may be measured , either by the perp . CD , or the arc BQ . Let NESQ be a ...
Página 41
... constructed by aid of Prop . 47 , Book I. D E B PROP . 18. - THEOR . If a st . line touches a circle , the st . line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle . CON . 1 , III ...
... constructed by aid of Prop . 47 , Book I. D E B PROP . 18. - THEOR . If a st . line touches a circle , the st . line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle . CON . 1 , III ...
Página 48
... constructing innumerable triangles fulfilling these two con- ditions , the vertices would form the segment of a circle ... construct a figure representative of the distance of the place of observation from an object . and Ex . - Three ...
... constructing innumerable triangles fulfilling these two con- ditions , the vertices would form the segment of a circle ... construct a figure representative of the distance of the place of observation from an object . and Ex . - Three ...
Página 49
... construct the AABC ; at C make ACE = 19 ° BDA , and at A , △ CAE = 25 ° = △ CDB ; and through the three points A , E , and C , ( Prop . 3. Use 4 , III . ) draw a circle ADCE ; A join BE , and produce it to intersect the circle in D ...
... construct the AABC ; at C make ACE = 19 ° BDA , and at A , △ CAE = 25 ° = △ CDB ; and through the three points A , E , and C , ( Prop . 3. Use 4 , III . ) draw a circle ADCE ; A join BE , and produce it to intersect the circle in D ...
Página 51
... construct the Tables of Chords ; and in Trigonometry it may be applied to prove that the sides of an obtuse angled triangle have the same ratio to one another as the sines of their opposite angles ; and hence , if any three be given ...
... construct the Tables of Chords ; and in Trigonometry it may be applied to prove that the sides of an obtuse angled triangle have the same ratio to one another as the sines of their opposite angles ; and hence , if any three be given ...
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Euclid's Plane Geometry, Books III.-VI., Practically Applied; Or, Gradations ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD Antecs Arith base bisected centre chord circumference circumscribed compd Conc contained decagon desc diam diameter distance divided draw drawn equiangular equims equimultiples Euclid extreme four magnitudes fourth Geometry given circle given line given st greater hypotenuse inscribed isosc join less mean measure multiple parallel parallelogram pentagon perp Plane Geometry polygon PROB Prop propl proportional proposition Quæs radius ratio compounded rect rectangle rectil rectilineal figure regular polygon Remk segments semic semiperimeter sides similar square star-shaped polygon straight line tang tangent third touch triangle vertex
Pasajes populares
Página 7 - If two triangles have two sides of the one equal to two sides of the...
Página 151 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any...
Página 81 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 85 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Página 310 - 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 11 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Página 33 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Página 156 - XIII. Permutando, or alternando, by permutation, or alternately; this word is used when there are four proportionals, and it is inferred, that the first has the same ratio to the third, which the second has to the ,fourth; or that the first is to the third, as the second to the fourth; as is shown in the 16th prop.
Página 219 - If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ratio which the first of the others has to the last. NB This is usually cited by the words "ex sequali,
Página 216 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words