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
... described from any given point as centre , at any given dis- tance from that centre ; or , what is the same thing , with any given point as centre , and with any given finite straight line drawn from that point as radius . AXIOMS . I ...
... described from any given point as centre , at any given dis- tance from that centre ; or , what is the same thing , with any given point as centre , and with any given finite straight line drawn from that point as radius . AXIOMS . I ...
Página 11
... described on the given straight line AB . Which was to be done . : PROP . II . PROB . 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 ...
... described on the given straight line AB . Which was to be done . : PROP . II . PROB . 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 ...
Página 57
... described a parallelogram HECK equal to the given tri- angle ABC , and having an angle HEC equal to the given angle D. Which was to be done . PROP . XLMI . THEOR . If through any point in one of the diagonals of a parallelogram , two ...
... described a parallelogram HECK equal to the given tri- angle ABC , and having an angle HEC equal to the given angle D. Which was to be done . PROP . XLMI . THEOR . If through any point in one of the diagonals of a parallelogram , two ...
Página 62
... described on the given straight line Which was to be done . AB . COR . - Every parallelogram that has one of its angles a right angle shall have all its angles right angles . Let ABCD be a parallelogram , and let it have 62 [ воок THE ...
... described on the given straight line Which was to be done . AB . COR . - Every parallelogram that has one of its angles a right angle shall have all its angles right angles . Let ABCD be a parallelogram , and let it have 62 [ воок THE ...
Página 63
... described on the sides including the right angle . Let ABC be a right - angled triangle having the right angle BAC . Then the square described on the side BC , opposite to the right angle BAC , shall be equal to the squares described on ...
... described on the sides including the right angle . Let ABC be a right - angled triangle having the right angle BAC . Then the square described on the side BC , opposite to the right angle BAC , shall be equal to the squares described on ...
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.