Elements of geometry: consisting of the first four,and the sixth, books of Euclid, with the principal theorems in proportion [&c.] by J. Narrien1842 |
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Αποτελέσματα 1 - 5 από τα 56.
Σελίδα
... consequently bisecting it in D. Then , if AB be an assignable line , its half , AD , will be assignable , and AD2 will be an assign- able surface : but AD2 AC2 - CD2 = ( AC + CD ) . ( AC - CD ) = ( AC + CD ) . DE ; D E B therefore DE is ...
... consequently bisecting it in D. Then , if AB be an assignable line , its half , AD , will be assignable , and AD2 will be an assign- able surface : but AD2 AC2 - CD2 = ( AC + CD ) . ( AC - CD ) = ( AC + CD ) . DE ; D E B therefore DE is ...
Σελίδα 16
... consequently ( 4. 1. ) the angle CHF is equal to CHG . Therefore these are right angles , and CH is perpendicular to AB . When the given point c is nearly opposite one extremity of the given line . From any convenient point N in the ...
... consequently ( 4. 1. ) the angle CHF is equal to CHG . Therefore these are right angles , and CH is perpendicular to AB . When the given point c is nearly opposite one extremity of the given line . From any convenient point N in the ...
Σελίδα 17
... consequently , that all the angles made by any number of lines meeting in one point , are together equal to four right angles . PROP . XIV . THEOR . IF , at a point in a straight line , two other straight lines , upon the opposite sides ...
... consequently , that all the angles made by any number of lines meeting in one point , are together equal to four right angles . PROP . XIV . THEOR . IF , at a point in a straight line , two other straight lines , upon the opposite sides ...
Σελίδα 40
... consequently to the given rectilineal figure . PROP . XLVI . PROB . To describe a square upon a given straight line . Let AB be the given straight line : it is required to describe a square upon A B. C From the point a draw ( 11. 1 ...
... consequently to the given rectilineal figure . PROP . XLVI . PROB . To describe a square upon a given straight line . Let AB be the given straight line : it is required to describe a square upon A B. C From the point a draw ( 11. 1 ...
Σελίδα 80
... consequently the E B F two other angles BAD , ABD are equal ( 32. 1. ) to a right angle : but ABF is likewise a right angle ; therefore the angle ABF is equal to the angles BAD , ABD . Take from these equals the common angle ABD ...
... consequently the E B F two other angles BAD , ABD are equal ( 32. 1. ) to a right angle : but ABF is likewise a right angle ; therefore the angle ABF is equal to the angles BAD , ABD . Take from these equals the common angle ABD ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles altitudes angle ABC angle ACB angle BAC assigned base BC bisected centre circle ABC circumference cone convex surface cylinder described diameter draw drawn duplicate ratio Edition equal angles equal or equivalent equi equilateral and equiangular Euclid exterior angle fore given line given rectilineal given straight line gnomon greater Greek homologous homologous sides inscribed join Latin Let ABC measure number of sides opposite angles parallel parallelepiped parallelogram perpendicular picket plane angles prism PROB proportional proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure regular polygon remaining angle right angles segment similar solid angle sphere spherical angle square of AC straight line AC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 55 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Σελίδα 47 - CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line, &c.
Σελίδα 12 - 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 73 - CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED.
Σελίδα 8 - A New Treatise on the Use of the Globes ; or, a Philosophical View of the Earth and Heavens : comprehending an Account of the Figure, Magnitude, and Motion of the Earth: with the Natural Changes of its Surface, caused by Floods, Earthquakes, &c.
Σελίδα 142 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 11 - ABC is therefore equal to the remaining angle ACB, which are the angles at the base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore, " the angles at the base
Σελίδα 53 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 30 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Σελίδα 9 - If two triangles have two sides of the one equal to two sides of the...