The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Βιβλίο 11853 |
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Αποτελέσματα 1 - 5 από τα 60.
Σελίδα 2
... angle is the inclination of two lines to one another in a plane , which meet together in a point , but are not in the same direction . IX . A plane rectilinear angle ... BAČ ; the B E Fig . 1 . Fig . 2 . F angle included by the straight lines ...
... angle is the inclination of two lines to one another in a plane , which meet together in a point , but are not in the same direction . IX . A plane rectilinear angle ... BAČ ; the B E Fig . 1 . Fig . 2 . F angle included by the straight lines ...
Σελίδα 13
... angle BAC included by the two sides BA , AC of the one equal to the angle EDF included by the two sides ED , DF of the other . Then these triangles shall be equal in every respect : i . e . ( 1 ) the base BC shall be equal to the base ...
... angle BAC included by the two sides BA , AC of the one equal to the angle EDF included by the two sides ED , DF of the other . Then these triangles shall be equal in every respect : i . e . ( 1 ) the base BC shall be equal to the base ...
Σελίδα 14
... angle BAC is equal to the angle EDF by hyps ; and the triangles fall by const " on the same side of DE : hence also the point c coincides with the point F , because AC is equal to DF by hyps : But the point B was shewn to coincide with ...
... angle BAC is equal to the angle EDF by hyps ; and the triangles fall by const " on the same side of DE : hence also the point c coincides with the point F , because AC is equal to DF by hyps : But the point B was shewn to coincide with ...
Σελίδα 17
... angle DBC equal to the in- cluded angle ACB . Therefore they are equal ( i . 4 ) in every respect ; and hence the ... B A C viz . AC , AB , are equal . Again , since the triangle is equiangular , the angle ABC is equal to the angle CAB ...
... angle DBC equal to the in- cluded angle ACB . Therefore they are equal ( i . 4 ) in every respect ; and hence the ... B A C viz . AC , AB , are equal . Again , since the triangle is equiangular , the angle ABC is equal to the angle CAB ...
Σελίδα 20
... angles EFD , FDE , DEF respectively : and the triangle ABC coincides with , and is therefore equal to , Which was to be proved . DEF . PROP . IX . PROB . To bisect a given angle , i . e . to divide it into two equal angles . Let BAC be ...
... angles EFD , FDE , DEF respectively : and the triangle ABC coincides with , and is therefore equal to , Which was to be proved . DEF . PROP . IX . PROB . To bisect a given angle , i . e . to divide it into two equal angles . Let BAC be ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.