...658. The volumes of two triangular pyramids, having a trihedral angle of the one equal to a trihedral angle of the other, are to each other as the products of the three edges of these trihedral angles. Let V and V denote the volumes of the two triangular pyramids...

...THEOBEM 397. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. A Given the A ABC and ADF having ZA in common/ _, A ABC ABXAC T°prOVe ~K~ADF'= ADXAF Proof. Draw the...

...altitudes. 397. // two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. 398. The areas of any two similar triangles are to each other as the squares of any two homologous...

...658. The volumes of two triangular pyramids, having a trihedral angle of the one equal to a trihedral angle of the other, are to each other as the products of the three edges of these trihedral angles. Let V and V denote the volumes of the two triangular pyramids...

...THEOREM 39 7 . If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Given the A ABC and ADF having1 /.A inocommon/ _ A ABC_ABXAO To prove A~TD^~ ADXAF' Proof, Draw the...

...Wendell Phillips HS, Chicago using the theorem: two triangles having an angle "f one equal to an agle of the other are to each other as the products of the sides including the equal angles; and by .\'. Anning, Ann Arbor. Mich., using BD/DC = ABDA/AADO = ABDO/AODC = ABOA/ AAOC; CE/EA ,= ACOB/ABOA;...

...from two intersecting lines. 4. Two tetraedrons which haVe a tricdral angle of one equal to a triedral angle of the other are to each other as the products of the three edges about the equal triedral angles. 5. Find the volume of a regular tetraedron whose edge...

...by the previous theorems. 198 PROPOSITION VII. THEOREM 414 Two triangles which have an angle of the one equal to an angle of the other are to each other...products of the sides including the equal angles. HYPOTHESIS. The & ABC and ADE have the ZA common. A ABC AB x AC CONCLUSION. A ADE AD x AE PROOF Draw...

...straight angle. (Necessary to prove propositions concerning concurrent lines.) *P16. Triangles that have an angle of one equal to an angle of the other, are to each other as the products of the sides containing those angles. *P18. In any obtuse triangle, the square of the side opposite the obtuse angle...

...THEOREM 675 The volumes of two tetraedrons, having a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles. HYPOTHESIS. V and V are the volumes of the two tetraedrons...