The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Libro 11853 |
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Página 160
... homologous to one another , and the second and fourth are called the conse- quents , and are likewise said to be homologous to one another . POSTULATES . I. Let it be granted that of a given magnitude there may be taken any multiple ...
... homologous to one another , and the second and fourth are called the conse- quents , and are likewise said to be homologous to one another . POSTULATES . I. Let it be granted that of a given magnitude there may be taken any multiple ...
Página 198
... homologous terms ( v . Def . 12 ) in the different proportions are called homolo- gous sides . Thus in Ex . I there are three pairs of homologous sides , viz . AB and DE ; BC and EF ; AC and DF . And in Ex . 2 there are five pairs of ...
... homologous terms ( v . Def . 12 ) in the different proportions are called homolo- gous sides . Thus in Ex . I there are three pairs of homologous sides , viz . AB and DE ; BC and EF ; AC and DF . And in Ex . 2 there are five pairs of ...
Página 207
... homologous in each proportion . Let the two triangles ABC , DEF have the angles ABC , BCA respectively equal to the angles DEF , EFD , and conse- quently ( i . 32. Cor . A ) the third angle BAC to the third angle EDF . Then these ...
... homologous in each proportion . Let the two triangles ABC , DEF have the angles ABC , BCA respectively equal to the angles DEF , EFD , and conse- quently ( i . 32. Cor . A ) the third angle BAC to the third angle EDF . Then these ...
Página 208
... homologous in each proportion , viz . AB shall be to BC as DE is to EF , BC to CA as EF to FD , and BA to AC as ED to DF . Apply the triangle DEF to the triangle ABC , so that the two sides BC , EF , opposite to a pair of equal an- gles ...
... homologous in each proportion , viz . AB shall be to BC as DE is to EF , BC to CA as EF to FD , and BA to AC as ED to DF . Apply the triangle DEF to the triangle ABC , so that the two sides BC , EF , opposite to a pair of equal an- gles ...
Página 209
... homologous sides in the proportions are opposite . Let the two triangles ABC , DEF have their sides about each of the three pairs of angles proportional , viz . let ab be to BC as DE is to EF , BC to CA as EF to FD , and con- sequently ...
... homologous sides in the proportions are opposite . Let the two triangles ABC , DEF have their sides about each of the three pairs of angles proportional , viz . let ab be to BC as DE is to EF , BC to CA as EF to FD , and con- sequently ...
Términos y frases comunes
ABC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles are equal angular points base BC bisected centre circle ABC circle DEF circumference const cut the circle diagonal draw equal angles equal Ax equals add equi equimultiples exterior angle FGHKL fore four magnitudes fourth given straight line gnomon hence the angle homologous hyps included angle interior and opposite join less Let ABC multiple opposite angle parallelogram perpendicular produced PROP proportional proved radius rectangle contained remaining angle respectively equal right angles segment shewn sides BC similar solid angle square of AC THEOR thing are equal third angle three angles touching the circle triangle ABC unequal
Pasajes populares
Página 39 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Página 52 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.
Página 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Página 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Página 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Página 66 - 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.
Página 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Página 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.