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 56.
Σελίδα 27
... similar to that of the first case . " Hence the opposite vertical angles AEC , BED are equal , and the opposite vertical angles BEC , AED are equal . Which was to be proved . COR . 1. — If two straight lines cut one another : then the ...
... similar to that of the first case . " Hence the opposite vertical angles AEC , BED are equal , and the opposite vertical angles BEC , AED are equal . Which was to be proved . COR . 1. — If two straight lines cut one another : then the ...
Σελίδα 62
... similar proof that the resulting figure is a parallelogram fulfilling the requisites of the problem . PROP . XLVI . PROB . To describe a square on a given straight line . Let AB be a given straight line . It is required to describe a ...
... similar proof that the resulting figure is a parallelogram fulfilling the requisites of the problem . PROP . XLVI . PROB . To describe a square on a given straight line . Let AB be a given straight line . It is required to describe a ...
Σελίδα 70
... similar to those in ( I. ) , the const here com- mencing by describing the square on ac , instead of BC . Which was to be proved . PROP . IV . THEOR . If a straight line be divided into any two parts : then the square of the whole line ...
... similar to those in ( I. ) , the const here com- mencing by describing the square on ac , instead of BC . Which was to be proved . PROP . IV . THEOR . If a straight line be divided into any two parts : then the square of the whole line ...
Σελίδα 78
... similar manner by producing BA and proceeding in the const " as before , it may be shewn that four times the rectangle BA , AC together with the square of BC is equal to the square of the line made up of BA and AC . was to be proved ...
... similar manner by producing BA and proceeding in the const " as before , it may be shewn that four times the rectangle BA , AC together with the square of BC is equal to the square of the line made up of BA and AC . was to be proved ...
Σελίδα 89
... by two radii , and the arc intercepted between them . Segments of cir- cles are defined to be similar , when the angles in them are equal . XI . PROPOSITIONS . PROP . I. THEOR . To find the 13 III . ] 89 DEFINITIONS .
... by two radii , and the arc intercepted between them . Segments of cir- cles are defined to be similar , when the angles in them are equal . XI . PROPOSITIONS . PROP . I. THEOR . To find the 13 III . ] 89 DEFINITIONS .
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.