The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Libro 11853 |
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Resultados 1-5 de 74
Página 6
... opposite sides equal , but all its sides are not equal , and its angles are not right angles . XXXIV . Trapeziums are such four - sided figures as are not included in the four preceding definitions . XXXV . Parallel straight lines are ...
... opposite sides equal , but all its sides are not equal , and its angles are not right angles . XXXIV . Trapeziums are such four - sided figures as are not included in the four preceding definitions . XXXV . Parallel straight lines are ...
Página 10
... side of EH towards A , C , that being the side on which the angles AFG , FGC are that are together less than two right angles ... opposite to one another , and on different sides of the cutting line , are called alternate inte- rior , or ...
... side of EH towards A , C , that being the side on which the angles AFG , FGC are that are together less than two right angles ... opposite to one another , and on different sides of the cutting line , are called alternate inte- rior , or ...
Página 13
... sides are opposite ; ( 3 ) the triangles shall be equal . Let ABC , DEF be two triangles , which have ( 1 ) the two sides BA , AC of the one re- spectively equal to the two sides ED , DF of the other , viz . BA to ED , and ac to DF ; AA ...
... sides are opposite ; ( 3 ) the triangles shall be equal . Let ABC , DEF be two triangles , which have ( 1 ) the two sides BA , AC of the one re- spectively equal to the two sides ED , DF of the other , viz . BA to ED , and ac to DF ; AA ...
Página 14
... opposite , shall be equal ; and ACB , DFE , to which the equal sides AB , DE are opposite , shall be equal ; ( 3 ) the triangle ABC shall be equal to the triangle DEF . Let the triangle ABC be applied to the triangle DEF , so that the ...
... opposite , shall be equal ; and ACB , DFE , to which the equal sides AB , DE are opposite , shall be equal ; ( 3 ) the triangle ABC shall be equal to the triangle DEF . Let the triangle ABC be applied to the triangle DEF , so that the ...
Página 16
... sides which subtend or are opposite to the equal angles shall be equal . Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AC shall be equal to the side AB . For if AB , AC be not equal , let them , if ...
... sides which subtend or are opposite to the equal angles shall be equal . Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AC shall be equal to the side AB . For if AB , AC be not equal , let them , if ...
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.