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 7
... angular points A , C , is one diagonal ; and BD , which joins the opposite angular points B , D , is the other diagonal . B A D A D A D C B C B C This def1 . , and Bk . ii . Def . 1 , have superseded Defs . 31 , 32 , 33 . POSTULATES . I ...
... angular points A , C , is one diagonal ; and BD , which joins the opposite angular points B , D , is the other diagonal . B A D A D A D C B C B C This def1 . , and Bk . ii . Def . 1 , have superseded Defs . 31 , 32 , 33 . POSTULATES . I ...
Página 46
... angular points of the figure . E A Ꭰ C F B There are as many trian- gles FAB , FBC , FCD , FDE , FEA having a common angular point F as the polygon ABCDE has sides ; and the angles of each of these triangles by the prop " are equal to ...
... angular points of the figure . E A Ꭰ C F B There are as many trian- gles FAB , FBC , FCD , FDE , FEA having a common angular point F as the polygon ABCDE has sides ; and the angles of each of these triangles by the prop " are equal to ...
Página 47
... angular point F , viz . AFB , BFC , CFD , DFE , EFA . But the angles at the bases of the triangles , viz . FAB , FBA ... points : then all the exterior angles shall be together equal to four right angles . Let ABCDE be any po- lygon ...
... angular point F , viz . AFB , BFC , CFD , DFE , EFA . But the angles at the bases of the triangles , viz . FAB , FBA ... points : then all the exterior angles shall be together equal to four right angles . Let ABCDE be any po- lygon ...
Página 48
... angular points , that is , as it has sides . But all the interior angles together with four right angles ( by Cor . 1 ) are equal to twice as many right angles as the polygon has sides ; and things that are equal to the same thing are ...
... angular points , that is , as it has sides . But all the interior angles together with four right angles ( by Cor . 1 ) are equal to twice as many right angles as the polygon has sides ; and things that are equal to the same thing are ...
Página 60
... angular points as DF of the polygon , so as to divide it into the two triangles CDF , DFE . To the straight line AB apply ( i . 44 ) the parallelogram ABHK , equal to the triangle CDF , and having one of its an- gles ABH equal to the ...
... angular points as DF of the polygon , so as to divide it into the two triangles CDF , DFE . To the straight line AB apply ( i . 44 ) the parallelogram ABHK , equal to the triangle CDF , and having one of its an- gles ABH equal to the ...
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.